Solution for the question - the range of the function f(x)=sqrt((x-1)(3-x)) is (-3,1) '/> (-3,3) '/> (-1,1) '/> [0,1] '/>

Maths-

General

Easy

Question

The range of the function $f left parenthesis x right parenthesis equals square root of left parenthesis x minus 1 right parenthesis left parenthesis 3 minus x right parenthesis end root text is end text$

$[0, 1]$
$(- 1, 1)$
$(- 3, 3)$
$(- 3, 1)$

hint Hint:

Here we have to find the range of f(x)= $square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root$ . Just solve the function and find the solution then find the range for the function.

The correct answer is: $left square bracket 0 comma 1 right square bracket$

Here we have to find that the range of $square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root$
f (x) = $square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root$
= $square root of negative x 2 plus 4 x minus 3 end root$
= $square root of negative x 2 plus 4 x minus 4 plus 1 end root$
= $square root of 1 minus open parentheses x minus 2 close parentheses 2 end root$
The maximum value of f (x) is 1,
when (x – 2) = 0.
So, we can write Fmax= 1
Now,
It is minimum when,
(x – 2)2 = 1
(x – 2) = ± 1 [ since, x = √a², then x = ± a]
At, positive, x -2 = 1 => x = 3
And at negative, x -2 = -1 => x = 1,
Therefore, x = 3, x = 1
So, Minimum = $square root of 1$ – 1 = 0
Therefore, the Range = [0, 1].

In this question, we have to find the range of f(x)= $square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root$ . Here solve the function and find when function is at maximum and minimum.

The range of the function $sin invisible function application open parentheses sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x close parentheses comma vertical line x vertical line less or equal than 1 text is end text$

maths-General

General

maths-

The domain of the function $f left parenthesis x right parenthesis equals log subscript e invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis text is end text$

maths-General

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maths-

If $n element of N$ , and the period of $fraction numerator cos invisible function application n x over denominator sin invisible function application open parentheses x over n close parentheses end fraction$ is $4 pi$ , then n is equal to

maths-General

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maths-

Domain of definition of the function $f left parenthesis x right parenthesis equals fraction numerator 3 over denominator 4 minus x squared end fraction plus log subscript 10 invisible function application open parentheses x cubed minus x close parentheses comma text is end text$

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$text If end text f left parenthesis x right parenthesis equals open parentheses fraction numerator x over denominator 1 minus vertical line x vertical line end fraction close parentheses to the power of 1 divided by 2002 end exponent comma text then end text D subscript f text is end text$

maths-General

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maths-

Range of the function $f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text$

maths-General

General

maths-

Range of the function $f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text$

maths-General

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maths-

The domain of $sin to the power of negative 1 end exponent invisible function application open parentheses log subscript 3 invisible function application x close parentheses text is end text$

maths-General

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The domain of the function $f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript invisible function application open parentheses x squared minus 1 close parentheses text is end text$

maths-General

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If $f left parenthesis x right parenthesis equals 2 x to the power of 6 plus 3 x to the power of 4 plus 4 x squared$ , then $f to the power of straight prime left parenthesis x right parenthesis$ is

Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables. A constant function has zero derivatives. For instance, f'(x) = 0 if f(x) = 8. So the derivative function is odd.

If $f left parenthesis x right parenthesis equals 2 x to the power of 6 plus 3 x to the power of 4 plus 4 x squared$ , then $f to the power of straight prime left parenthesis x right parenthesis$ is

Maths-General

General

maths-

The domain of the function $f left parenthesis x right parenthesis equals log subscript 2 invisible function application open parentheses log subscript 3 invisible function application open parentheses log subscript 4 invisible function application x close parentheses close parentheses$ is

maths-General

General

maths-

$text If end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text then, domain of end text f left parenthesis x right parenthesis text is end text$

maths-General

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maths-

The domain of the function $f left parenthesis x right parenthesis equals exp invisible function application open parentheses square root of 5 x minus 3 minus 2 x squared end root close parentheses$ is

maths-General

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The value of $tan invisible function application open curly brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 2 over 7 close parentheses minus pi over 2 close curly brackets$ is

maths-General

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$sin invisible function application open parentheses 1 half cos to the power of negative 1 end exponent invisible function application 4 over 5 close parentheses$ is equal to

maths-General

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The range of the function

Here we have to find the range of f(x)= . Just solve the function and find the solution then find the range for the function.

The correct answer is:

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The range of the function $f left parenthesis x right parenthesis equals square root of left parenthesis x minus 1 right parenthesis left parenthesis 3 minus x right parenthesis end root text is end text$

Here we have to find the range of f(x)= $square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root$ . Just solve the function and find the solution then find the range for the function.

The correct answer is: $left square bracket 0 comma 1 right square bracket$

The domain of the function $f left parenthesis x right parenthesis equals log subscript e invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis text is end text$

The domain of the function $f left parenthesis x right parenthesis equals log subscript e invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis text is end text$

If $n element of N$ , and the period of $fraction numerator cos invisible function application n x over denominator sin invisible function application open parentheses x over n close parentheses end fraction$ is $4 pi$ , then n is equal to

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Range of the function $f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text$

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The domain of the function $f left parenthesis x right parenthesis equals log subscript 2 invisible function application open parentheses log subscript 3 invisible function application open parentheses log subscript 4 invisible function application x close parentheses close parentheses$ is

The domain of the function $f left parenthesis x right parenthesis equals exp invisible function application open parentheses square root of 5 x minus 3 minus 2 x squared end root close parentheses$ is

The domain of the function $f left parenthesis x right parenthesis equals exp invisible function application open parentheses square root of 5 x minus 3 minus 2 x squared end root close parentheses$ is

The value of $tan invisible function application open curly brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 2 over 7 close parentheses minus pi over 2 close curly brackets$ is

The value of $tan invisible function application open curly brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 2 over 7 close parentheses minus pi over 2 close curly brackets$ is

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