Maths-

General

Easy

Question

Let $f colon R rightwards arrow R$ be given by $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis to the power of 2 end exponent minus 1 comma x greater or equal than negative 1$ . Then the set of values of x for which $f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is given by

{0}
{-1,0}
${- 1}$ {0}
{0,1}

hint Hint:

$f colon R rightwards arrow R$ indicates a function “f”, Having domain ”R” and co-domain “R” (Range). That means in simple we can imagine that “The set of all possible input values for x is the domain of the function. The set of all output values of y is the range of the function.”

The correct answer is: {-1,0}

The given function $f colon R rightwards arrow R$ be given by $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis to the power of 2 end exponent minus 1 comma x greater or equal than negative 1$
Indicates f(x) will satisfy all values for x $greater or equal than space minus 1$
$w e space h a v e space t o space p r o v e space space f left parenthesis x right parenthesis space equals space f to the power of negative 1 end exponent left parenthesis x right parenthesis space f to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction space equals space fraction numerator 1 over denominator left parenthesis x space plus space 1 right parenthesis squared minus 1 end fraction f o r space space f left parenthesis x right parenthesis space equals space f to the power of negative 1 end exponent left parenthesis x right parenthesis space comma space t h e space r e v e r s e space f u n c t i o n space s h o u l d space a l s o space h o l d space t h e space s a m e space v a l u e s space i. e space x space greater or equal than space minus 1 s u b s t i t u t i n g space left parenthesis 0 comma negative 1 right parenthesis space i n space f to the power of negative 1 end exponent left parenthesis x right parenthesis space comma space w e space g e t space f to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space minus 1 space equals space f left parenthesis x right parenthesis space$
Thus, the set of values of x for which $f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is given by (0, -1) for x $greater or equal than$ -1 .

If $1 minus e to the power of fraction numerator 1 over denominator x end fraction minus 1 end exponent greater than 0$ , then x is not satisfied by number of integral values

Maths-General

General

Maths-

The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

Maths-General

General

Maths-

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

Maths-General

We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

General

Maths-

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

Maths-General

General

physics

A Shell of mass M and radius R has a point mass placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

physicsGeneral

General

Physics

The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

PhysicsGeneral

General

physics

The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

physicsGeneral

General

chemistry-

Which of the following structures have same configuration around the chirality centre ?

chemistry-General

General

chemistry-

The two structures given below are :

chemistry-General

General

chemistry-

Which of the following represents same enantiomer as :

chemistry-General

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Let be given by . Then the set of values of x for which is given by

{0} {-1,0} {0} {0,1}

indicates a function “f”, Having domain ”R” and co-domain “R” (Range). That means in simple we can imagine that “The set of all possible input values for x is the domain of the function. The set of all output values of y is the range of the function.”

The correct answer is: {-1,0}

The given function be given by Indicates f(x) will satisfy all values for x Thus, the set of values of x for which is given by (0, -1) for x -1 .

Related Questions to study

If , then x is not satisfied by number of integral values

If , then x is not satisfied by number of integral values

The domain of is

The domain of is

The inverse of the function is

The inverse of the function is

The domain of is

The domain of is

A Shell of mass M and radius R has a point mass placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

A Shell of mass M and radius R has a point mass placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

The absolute configuration of the following compound is :

The absolute configuration of the following compound is :

The name of the compound is

The name of the compound is

Among the following structures which one is called Erythro isomer ?

Among the following structures which one is called Erythro isomer ?

How many stereo isomers are there in this compound ?

How many stereo isomers are there in this compound ?

The compound is known by which of the following names ?

The compound is known by which of the following names ?

Which of the following structures have same configuration around the chirality centre ?

Which of the following structures have same configuration around the chirality centre ?

The two structures given below are :

The two structures given below are :

Which of the following represents same enantiomer as :

Which of the following represents same enantiomer as :

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{0}
{-1,0}
${- 1}$ {0}
{0,1}

$f colon R rightwards arrow R$ indicates a function “f”, Having domain ”R” and co-domain “R” (Range). That means in simple we can imagine that “The set of all possible input values for x is the domain of the function. The set of all output values of y is the range of the function.”

If $1 minus e to the power of fraction numerator 1 over denominator x end fraction minus 1 end exponent greater than 0$ , then x is not satisfied by number of integral values

If $1 minus e to the power of fraction numerator 1 over denominator x end fraction minus 1 end exponent greater than 0$ , then x is not satisfied by number of integral values

The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is