We have been given that f be a differentiable function such that $f(3)=15$ , $f(6)=3$ , $f'(3)= -8$ , and $f'(6)= -2$ . The function g is differentiable and $g(x)= f^{-1} (x)$ for all x.

We know that when one function is inverse of other function, so:

$g(f(x))=x$

Upon taking derivative of both sides of our equation, we will get:

$g'(f(x))*f'(x) =1$

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

Plugging $x=6$ into our equation, we will get:

$g'(f(6))=\frac{1}{f'(6)}$

Since $g(x)= f^{-1} (x)$ , then $g'(f(6))=g'(3)$ .

$g'(3)=\frac{1}{f'(6)}$

Since we have been given that $f'(6)= -2$ , so we will get:

$g'(3)=\frac{1}{-2}$

$g'(3)=-\frac{1}{2}$

Therefore, $g'(3)=-\frac{1}{2}$ and option A is the correct choice.

8 0

3 years ago

Samuel paid $25.82 for gas this week, which was $3.47 less than he paid last week. How much had he paid last week?

Yuri [45]

Samuel was paid $29.29 last week.

Hope this helps

5 0

3 years ago