Question

Please answer correctly and I will mark your answer as brainliest and please don't spam

If g is the inverse function of f and
f'(x) =1 / (1 + x^n) then the value of g '(x) =

1) 1- (g(x))^n
2) [1 + g(x)]^n
3) 1 + (g(x))^n
4) (g(x))^n​

Answer 1

IF G IS INVERSE OF F THEN WE HAVE

.

$fogo(x) = x$

$f( g(x)) = x$

differentiating wrt x we get

$f '(g(x)) \times g '(x) = 1$

$\frac{1}{1 + (g(x))^{n} } \times g '(x) = 1$

$g '(x) = 1 + (g(x))^{n}$

NOW IF YOU DIDNT UNDERSTAND LAST SECOND STEP ITS EXPLANATION IS HERE

$he \: given \: that \\ f '(x) = \frac{1}{1 + {x}^{n} }$

substituting g(x) in place of x it gives

$f '(g(x)) = \frac{1}{1 +(g(x))^{n} }$

HERE YOU GO I HOPE YOU LIKE IT