Suppose that g is the inverse of a function F. If f (3) = 4 and f '(3) = 5, find g'0(4).

A)4
B)3

Question

Suppose that g is the inverse of a function F. If f (3) = 4 and f '(3) = 5, find g'0(4).

A)4 
B)3

Quizplus · Accepted Answer

Since g is the inverse of F, we have $g(F(x))=x$. Therefore, $g(f^{-1}(3))=3$ and $g(f^{-1}(5))=5$. We know that $f(3)=4$, so $f^{-1}(4)=3$. Thus, $g(4) = g(f(f^{-1}(4))) = f^{-1}(4)$.
Similarly, we know that $f(f(f(3))) = f(5) = S'(3)$, so $g(S'(3)) = f(f(3))$. Finally, $f(f(3))=f(4)=10$.
Therefore, $g(4)=f^{-1}(4)=3$ and $g(S'(3))=f(f(3))=10,$ so the answer is D.

Suppose That G Is the Inverse of a Function F