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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

If

g

is the inverse of a function

f

and

f'(x) = \frac{1}{{1 + {x^5}}},\,

then

g'(x)

is equal to

View answer and explanation

Correct option: D

1 + {\left\{ {g(x)} \right\}^5}

Option D (

1 + {\{ g(x)\} ^5}

) is correct because by differentiating

f(g(x)) = x

and using the given

f'(x)

, we can find

g'(x)

.

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f\left( x \right) = x - \left[ x \right]

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f(x)=x^4

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S=\left\{x: f(x)=f^{-1}(x)\right\}