Suppose g is the inverse function of f an f(7) = -2, f(-3) = 4, f'(7) = 1/2 and f'(-3) = -3/4. Find g'(4).

Question

Thank you for any help you can give me. I am struggling with inverse function in my calculus class and am studying for a test.

Answer 1

Hi Alex -

It helps to visualize the functions f and g as reflections of each other about the y = x diagonal on a coordinate grid. Every point on f has a corresponding point on g that is the same distance from y = x, but on the other side (along the line that goes perpendicular from the point to the diagonal. Not only that, the slopes of the 2 functions must also be symmetric with respect to y = x, which means their product will always be 1.

Since f(-3) = 4, we can say g(4) = -3

Also f'(-3) = -3/4, so the slope of g at 4 must be -4/3.

In summary, g'(4) = -4/3

Answer 2

Hi,

Suppose g is the inverse function of f an f(7) = -2, f(-3) = 4, f'(7) = 1/2 and f'(-3) = -3/4. Find g'(4).

first you need to know the meaning of inverse of function.

if g(x) is inverse f(x) we have:

f(7) = -2 ---> g(-2) =7

f(-3) = 4----> g(4) = -3

g'(x) = 1/f'(x) be careful, these x are not the same, x at the left side is out put (y) for f(x)

now we need to find g'(4) , but 4 is out put for function f, as a result f(-3) = 4

g'(4)= 1/f'(-3) and given information is f'(-3) = -3/4

g'(4) = -4/3

I hope it is useful, please let me know if you have any question.

Minoo