Question

If g(x) = 4 + x + e^x, find g^-1(5).
g^-1(5) =

The online homework does a horrible job at explaining the steps on how to solve this problem. If anyone can walk me through how to solve this problem that would be great.

Answer 1

Well, from what I've seen you're not expected to find the inverse function in those questions, just the specific value. So we ask ourselves, for what x will g(x) output 5?
Well, if we let x=0 we get \(4 + 0 + e^0 = 4 + 1 = 5\)
so \(g^{-1}(5) = 0\)

Answer 2

5 = 4 + x + e^x
1 = x + e^x

look at it now. what must x be?

bear in mind what y = x and y = e^x look like.