Questions: Graph the inverse of (g(x)).

Transcript text: Graph the inverse of $g(x)$.

Solution

Solution Steps

Step 1: Identify Key Points

The graph of $g(x)$ passes through the points $(-1, -1)$, $(0, 4)$, and $(1, 13)$.

Step 2: Swap the Coordinates

To find the inverse, we swap the x and y coordinates of the points on the graph of $g(x)$. The points on the graph of $g^{-1}(x)$ are thus $(-1, -1)$, $(4, 0)$, and $(13, 1)$.

Step 3: Plot and Connect the Points

Plot the points $(-1, -1)$, $(4, 0)$, and $(13, 1)$ on the graph and connect them with a smooth curve. The resulting curve is the graph of $g^{-1}(x)$.

Final Answer:

The graph of the inverse function $g^{-1}(x)$ passes through the points $(-1,-1)$, $(4,0)$, and $(13,1)$. The graph looks like the given graph of $g(x)$ reflected across the line $y=x$.

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