Method 1 will have us plug x = 0 into h(x) to get h(x) = x^2 - 4 h(0) = 0^2 - 4 h(0) = 0 - 4 h(0) = -4 Then this output is plugged into g(x) to get g(x) = 2x g(-4) = 2*(-4) g(-4) = -8 which is the answer This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4 So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8
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The second method involves a bit algebra first Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4
g(x) = 2x g(x) = 2( x ) g(h(x)) = 2( h(x) ) ... replace every x with h(x) g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4 g(h(x)) = 2x^2-8 (g o h)(x) = 2x^2-8
Now plug in x = 0 (g o h)(x) = 2x^2-8 (g o h)(0) = 2(0)^2-8 (g o h)(0) = 2(0)-8 (g o h)(0) = 0-8 (g o h)(0) = -8
Regardless of which method you use, the answer is -8
