Question

Given the definitions of f(x) and g(x) below, find the value of

(gof)(-4).
f(x) = x² + 2x – 14
g(x) = -x +7

Answer 1

To find the value of (gof)(-4), substitute -4 into the composite function gof by first finding the value of g(f(x)) and then substituting -4 into the resulting expression, which equals 13.

Step-by-step explanation:

To find the value of (gof)(-4), we need to substitute the value of -4 into the composite function gof. First, let's find the value of g(f(x)) by substituting f(x) into g(x):

g(f(x)) = g(x² + 2x - 14)

Now, substitute -4 into f(x) to get the value of g(f(-4)):

g(f(-4)) = g((-4)² + 2(-4) - 14) g(f(-4)) = g(16 - 8 - 14)

g(f(-4)) = g(-6)

Finally, substitute -6 into g(x) to get the final answer:

(gof)(-4) = g(f(-4)) = g(-6) = -(-6) + 7 = 6 + 7 = 13