Question

-5 -4 -3 -2 -1

g (g (-2)) =
f(-4)=
Y
3-
2
1+
7
-
-2+
3
Graph of g
2
3
4 5
The graph of the piecewise-linear
function g is shown in the figure. Let f
be the inverse function of g.
-X

Answer 1

Following the graph of g, g(-2) is 25, and since f is the inverse, f(-4) is g(25) which is 5.

Here's how we can find these values using the graph:

1. Finding g(g(-2))

Look for the point on the graph where the input is -2 (vertical axis). This point is at (-2, 19).

Follow the horizontal line from this point to the right until it intersects the graph again. This intersection point is at (5, 25).

Therefore, g(-2) = 19 and g(g(-2)) = 25.

2. Finding f(-4)

Look for the point on the graph where the output is -4 (horizontal axis). This point is not directly on the graph, but we can estimate it by looking for the horizontal line that intersects the graph slightly below -4. This line intersects the graph at (5, 25).

Since f is the inverse of g, the point (5, 25) on the graph of g becomes (25, 5) on the graph of f.

Therefore, f(-4) = 5.

In conclusion:

g(g(-2)) = 25

f(-4) = 5