Given that g is the inverse function of f, and f (3) = 4 , and f ′(3) =5 , then g′(4) =


-1/5

-3/5

3/5

Huh? Take a look at what I wrote!

f'(3) = 5
f(3) = 4
so, g'(4) = 1/f'(3) = 1/5

if f(a) = b then g'(b) = 1/f'(a)

Now just plug in your numbers

Okay so it is 1/4

To find g′(4), we need to use the fact that g is the inverse function of f.

First, we know that the inverse of a function reverses the roles of the input and output values. So if f(3) = 4, then g(4) = 3.

Next, we need to find the derivative of g. Since the derivative of the inverse function is equal to the reciprocal of the derivative of the original function, we can use this property to find g′(4).

Given that f ′(3) = 5, we can calculate g′(4) as follows:

g′(4) = 1 / f′(g(4))

Substituting in the value we found for g(4):

g′(4) = 1 / f′(3)

Therefore, g′(4) = 1 / 5. So, the answer is 1/5.