Q

# Try this! - Differential Calculus - BITSAT

The inverse of the function   $y=\left [ 1-\left ( x-3 \right )^{4} \right ]^{\frac{1}{7}}$  is

• Option 1)

$3+\left ( 1-x^{7} \right )^{\frac{1}{4}}$

• Option 2)

$3-\left ( 1+x^{7} \right )^{\frac{1}{4}}$

• Option 3)

$3-\left ( 1-x^{7} \right )^{\frac{1}{4}}$

• Option 4)

None of these

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As we learnt in

Co - Domain of function -

All possible outcomes for the function f(x) is known as co - domain unless not specified in question.

-

Range of function -

All possible values of  $f(x)\: \: \forall x\in$ domain  $(f)$ is known as Range

-

$y=\left [1 -(x-3)^{4} \right ]^\frac{1}{7}$

$y^{7}=1-(x-3)^{4}$

$\therefore (x-3)^{4}=1-y^{7}$

$x=3+(1-y^{7})^\frac{1}{4}$

$f^{-1}(x)=3+(1-x^{7})^\frac{1}{4}$

Option 1)

$3+\left ( 1-x^{7} \right )^{\frac{1}{4}}$

Option is correct

Option 2)

$3-\left ( 1+x^{7} \right )^{\frac{1}{4}}$

Option is incorrect

Option 3)

$3-\left ( 1-x^{7} \right )^{\frac{1}{4}}$

Option is incorrect

Option 4)

None of these

Option is incorrect

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