If g(x) = 3 + x + ex, 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 + ex, then g-1(4) = 0.
Let's solve this step by step.
Given that, g(x) = 3 + x + ex
g'(x) = 1 + ex > 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