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given the definitions of f(x) and g(x) below, find the value of f(g(-9)). f(x)=x^2-6x-9
g(x)=-2x-14

Respuesta :

Answer:   -17

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Explanation:

Let's evaluate the inner function g(-9) first.

Plug x = -9 into g(x). Simplify.

g(x) = -2x-14

g(-9) = -2*(-9) - 14

g(-9) = 18 - 14

g(-9) = 4

This means f(g(-9)) updates to f(4) because we can replace g(-9) with 4.

We'll repeat the same idea as above, but now pick on f(x). Plug in x = 4.

f(x) = x^2 - 6x - 9

f(4) = 4^2 - 6(4) - 9

f(4) = 16 - 24 - 9

f(4) = -8 - 9

f(4) = -17

Therefore, f(g(-9)) = -17

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