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If f(g(x)) = x and g(f(x)) = x then g(x)...

If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of `f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x))`
Let g(x) be the inverse of f(x) such that f'(x) `=1/(1+x^5)` ,then `(d^2(g(x)))/(dx^2)` is equal to

A

`1/(1+(g(x))^5)`

B

`(g'(x))/(1+(g(x))^5)`

C

`5(g(x))^4+(1+(g(x))^5)`

D

`1+g(x))^5`

Text Solution

Verified by Experts

The correct Answer is:
C
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