Question

Given the definitions of f, left bracket, x, right bracketf(x) and g, left bracket, x, right bracketg(x) below, find the value of left bracket, g, circle, f, right bracket, left bracket, 5, right bracket, .(g∘f)(5).

f, left bracket, x, right bracket, equals, x, squared, minus, x, minus, 14
f(x)=
x
2
−x−14
g, left bracket, x, right bracket, equals, minus, x, minus, 7
g(x)=
−x−7

Answer 1

To find the value of (g∘f)(5), substitute x = 5 into f(x) and g(x), then evaluate the composed function.

Step-by-step explanation:

To find the value of (g∘f)(5), we need to substitute the value of x = 5 into the composed function (g∘f).

First, we find f(5) by substituting x = 5 into the function f. f(x) = x^2 - x - 14, so f(5) = 5^2 - 5 - 14 = 25 - 5 - 14 = 6.

Then, we find g(f(5)) by substituting f(5) = 6 into the function g. g(x) = -x - 7, so g(f(5)) = g(6) = -(6) - 7 = -6 - 7 = -13.