If g(x) = 3 + x + e^x, find g^-1(4).

We will be using the concept of inverse function to solve this. The inverse of a function is a function that returns the original value (input value) for which a function has given the output value.

Answer: If g(x) = 3 + x + e^x, then g^-1(4) = 0.

Let's solve this step by step.

Explanation: 

Given that, g(x) = 3 + x + e^x 

g'(x) = 1 + e^x > 0

⇒ g(x) is an increasing function.

g(0) = 3 + 0 + e⁰

g(0) = 3 + 1

g(0) = 4

Using inverse function definition:

⇒  g^-1(4) = 0

Hence, if g(x) = 3 + x + e^x, then g^-1(4) = 0.