Question

Suppose f (x) = x3 + x and g(x) = f -1(x). Find g'(2).

Answer 1

what is the meaning of g(x)=f-1(x)
\[g(x)=\frac{ 1 }{ f(x) }\]?

Answer 2

inverse of f(x)

Answer 3

\[g(f(x)=x\\
g'(f(x))f'(x)=1\\
g'(f(1) f'(1) =1\\
g'(2)=\frac 1 {f'(1)}\]
Can you finish it?

Answer 4

\[
f(x)= x^3 + x\\
f'(x) = 3 x^2 +1\\
f'(1) =4\\
g'(2)=\frac 1 4
\]