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# 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 + e^{0}

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.

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