Solution for the question - f(x)=tan^(-1)x-x is decreasing in (-oo,0) '/> only (-1,1) '/> only (0,oo) '/> only (-oo,oo)'/>

Maths-

General

Easy

Question

$f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x minus x$ is decreasing in

$(- \infty, \infty)$
$(0, \infty)$ only
$(- 1,1)$ only
$(- \infty, 0)$ only

hint Hint:

We are given a function. We have to find the interval for which it is decreasing. We will take the first order derivative to find the answer

The correct answer is: $left parenthesis negative infinity comma infinity right parenthesis$

The given function is f(x) = tan^-1x - x
A function is said to be decreasing when it’s first order derivative is negative
It means f’(x) < 0
We will use this condition to find the answer.
Taking the first order derivative of the given function.
f(x) = tan^-1x - x
$f apostrophe left parenthesis x right parenthesis space equals fraction numerator 1 over denominator 1 plus x squared end fraction minus 1 f apostrophe left parenthesis x right parenthesis space less than space 0 rightwards double arrow fraction numerator 1 over denominator 1 space plus space x squared end fraction minus 1 space less than space 0 space space space space space space space space space space fraction numerator 1 space minus space 1 space minus x squared over denominator 1 space plus space x squared end fraction less than 0 space space space space space... left curly bracket space m a k i n g space t h e space d e n o m i n a t o r space e q u a l right curly bracket space space space space space space space space space space space space space space space space space fraction numerator negative x squared over denominator 1 space plus x squared end fraction less than 0 N o w comma space x squared space i s space t h e space p o s t i v e space q u a n t i t y space f o r space a n y space x element of R. space I t space m e a n s space f o r space a n y space r e a l space v a l u e space o f space x comma space x to the power of 2 space end exponent i s space a l w a y s space p o s i t i v e space space space space space space space space space space S o comma space t h e space t e r m space fraction numerator x squared over denominator 1 space plus space x squared end fraction space w i l l space b e space a l w a y s space p o s i t i v e.$
The negative sign make sures that the function is negative i.e. decreasing.
x can take any value of real number.
And the set of real numbers extends from -∞ to ∞.
So, the interval for which given function is decreasing is (-∞, ∞)

We should know the formulas of differentiation. And, we should know the condition for increasing and decreasing function.

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

For such questions, we should know different formulas of differentiation.

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

Maths-General

For such questions, we should know different formulas of differentiation.

General

physics-

In experiment of the potentiometer wire $A B$ of length 100 cm has a resistance of 10 $capital omega$ , It is connected in series with a resistance R and a cell of emf 2 volts and of negligible internal resistance. A Source of emf 10mV is balanced against a length of 40 cm of the potentiometer wire. What is the value of the external resistance?

physics-General

General

Maths-

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

For such questions, we should check the rules of increasing and decreasing function.

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

Maths-General

For such questions, we should check the rules of increasing and decreasing function.

General

maths-

If the function $fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction$ is decreasing in its domain then $K E$

maths-General

General

Maths-

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

We have to see the rules for a increasing and decreasing function.

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

Maths-General

We have to see the rules for a increasing and decreasing function.

General

maths-

If $l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1$ then the maximum value of $l plus m$ is

maths-General

General

maths-

The minimum value of the function $f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x$ where $x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ is

maths-General

General

physics-

In the experiment of potentiometer wire $A B$ is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

physics-General

General

physics-

Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

physics-General

General

physics-

Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point-A and zero-deflection is observed at length PJ=10 cm. In the second case, it is connected at a point $C$ and zero deflection is observed at a length $30 text end text c m$ from P. Then what is the unknown resistance X?

physics-General

General

physics-

The current taken from the 30 V supply and the current through the 6 $capital omega$ resistor are respectively.

physics-General

General

physics

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and $alpha$ =0.98

physicsGeneral

General

physics

The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

physicsGeneral

General

physics

In a transistor amplifier β=62, $R subscript L$ =5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

physicsGeneral

General

physics

In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

physicsGeneral

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

is decreasing in

only only only

We are given a function. We have to find the interval for which it is decreasing. We will take the first order derivative to find the answer

The correct answer is:

Related Questions to study

The interval of increase of the function is

The interval of increase of the function is

The function is

The function is

If the function is decreasing in its domain then

If the function is decreasing in its domain then

The function is

The function is

If then the maximum value of is

If then the maximum value of is

The minimum value of the function where is

The minimum value of the function where is

In the experiment of potentiometer wire is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

In the experiment of potentiometer wire is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

The current taken from the 30 V supply and the current through the 6 resistor are respectively.

The current taken from the 30 V supply and the current through the 6 resistor are respectively.

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and =0.98

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and =0.98

The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

In a transistor amplifier β=62,=5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

In a transistor amplifier β=62,=5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

$f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x minus x$ is decreasing in

$(- \infty, \infty)$
$(0, \infty)$ only
$(- 1,1)$ only
$(- \infty, 0)$ only

The correct answer is: $left parenthesis negative infinity comma infinity right parenthesis$

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

If the function $fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction$ is decreasing in its domain then $K E$

If the function $fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction$ is decreasing in its domain then $K E$

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

If $l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1$ then the maximum value of $l plus m$ is

If $l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1$ then the maximum value of $l plus m$ is

The minimum value of the function $f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x$ where $x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ is

The minimum value of the function $f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x$ where $x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ is

In the experiment of potentiometer wire $A B$ is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

In the experiment of potentiometer wire $A B$ is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

The current taken from the 30 V supply and the current through the 6 $capital omega$ resistor are respectively.

The current taken from the 30 V supply and the current through the 6 $capital omega$ resistor are respectively.

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and $alpha$ =0.98

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and $alpha$ =0.98

In a transistor amplifier β=62, $R subscript L$ =5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

In a transistor amplifier β=62, $R subscript L$ =5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?