Answer:
(a) -5
(b) 5
Explanation:
You want the values of h(k(-2)) and (k∘h)(0).
A) h(k(-2))
First, you find the value of k(-2) from the graph of y = k(x). On that graph, x=-2 is the line of symmetry, and (-2, -4) is the vertex of the parabola.
k(-2) = -4
Then you find h(-4). That value appears to be -5.
h(k(-2)) = -5
B) (k∘h)(0)
This composition is another way to write k(h(0)). First you find h(0). The line crosses the y-axis at y=1, so ...
h(0) = 1
Then you find k(1). That value appears to be +5.
(k∘h)(0) = 5
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Additional comment
The functions appear to be h(x) = 3/2x +1 and k(x) = (x +2)² -4. This makes the compositions be h(k(x)) = 3/2(x +2)² -5, and (k∘h)(x) = (3/2x +3)² -4.
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