If the function f(x)=x3+ex / 2 and g(x)=f-1(x), then the value of g prime(1) is

Question

If the function f(x)=x3+ex / 2 and g(x)=f-1(x), then the value of g prime(1) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(0)=1, f prime(x)=3 x2+(1/2) ex / 2 ⇒ f prime(g(x)) g prime(x)=1 Put x=0 ⇒ g prime(1)=(1/f prime(0))=2

Q. If the function $f (x) = x^{3} + e^{x /2}$ and $g (x) = f^{- 1} (x)$ , then the value of $g^{'} (1)$ is