if g(x)=f^(-1)(x), with f(7)=6 and g(7)=3, then g(7) equals -1/f(3) 1/f(6) -1/f(6) 1/f(3)

Answer:

$\frac{1}{f'(3)}$

Explanation:

Step1: Recall inverse - function derivative formula

If $g(x)=f^{-1}(x)$, then $g'(x)=\frac{1}{f'(g(x))}$.

Step2: Substitute $x = 7$

We want to find $g'(7)$. Using the formula $g'(x)=\frac{1}{f'(g(x))}$, when $x = 7$, we have $g'(7)=\frac{1}{f'(g(7))}$.

Step3: Use given value of $g(7)$

Since $g(7)=3$, then $g'(7)=\frac{1}{f'(3)}$.