Question

the graph of f(x) is shown below.
if g(x) and f(x) are inverse functions, which graph represents g(x)?

Explanation:

The graph of an inverse function $g(x)$ of $f(x)$ is the reflection of the graph of $f(x)$ across the line $y=x$. This means every point $(a,b)$ on $f(x)$ corresponds to a point $(b,a)$ on $g(x)$. The original $f(x)$ starts at $(0,0)$ and increases slowly, so $g(x)$ will start at $(0,0)$, increase, and be the mirror image over $y=x$.

Answer:

The graph that is the reflection of $f(x)$ across the line $y=x$ (i.e., swapping the $x$ and $y$ coordinates of all points on $f(x)$) represents $g(x)$. Visually, this is the mirror image of the given $f(x)$ graph over the diagonal line $y=x$.