Answer:
To find the composite function G(F(x)) using the given equation G(F(x)) = 5(x-7)²-4, we need to determine the function F(x) first.
Since the equation G(F(x)) is composed of two functions, we can see that F(x) represents the inner function, and G(x) represents the outer function.
In this case, F(x) = x-7 represents the inner function, and G(x) = 5x²-4 represents the outer function.
To find G(F(x)), we substitute F(x) into G(x) wherever we see x in the expression for G(x). So, we replace x in G(x) with (x-7).
G(F(x)) = 5((x-7)-7)²-4
Simplifying further:
G(F(x)) = 5(x-14)²-4
Therefore, the composite function G(F(x)) for the given equation is G(F(x)) = 5(x-14)²-4.