Problem 14

Given $f(x) = 5 - x$ and $g(x) = 2^x - 1$. Determine which of the following statements are correct:

1. $g(x)$ is a linear line with a gradient of $2$.
2. $f(x)$ and $g(x)$ intersect at $x > 0$.
3. $f(x)$ is above $g(x)$ for all values of $x$.
4. The graphs of $f(x)$ and $g(x)$ intersect at $(2, 3)$.