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Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, g, circle, f, right parenthesis, left parenthesis, 2, right parenthesis, .(g∘f)(2).f, of, x, equals, 2, x, minus, 8f(x)=2x−8g, of, x, equals, x, squared, plus, 7, x, plus, 9g(x)=x 2 +7x+9

Question

Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, g, circle, f, right parenthesis, left parenthesis, 2, right parenthesis, .(g∘f)(2).f, of, x, equals, 2, x, minus, 8f(x)=2x−8g, of, x, equals, x, squared, plus, 7, x, plus, 9g(x)=x 2 +7x+9

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Solution

To find the value of (gf)(2)(g \circ f)(2), we need to follow these steps:

  1. Evaluate f(2)f(2): Given f(x)=2x8f(x) = 2x - 8, f(2)=2(2)8=48=4 f(2) = 2(2) - 8 = 4 - 8 = -4

  2. Evaluate g(f(2))g(f(2)): We found that f(2)=4f(2) = -4. Now we need to find g(4)g(-4). Given g(x)=x2+7x+9g(x) = x^2 + 7x + 9, g(4)=(4)2+7(4)+9 g(-4) = (-4)^2 + 7(-4) + 9 =1628+9 = 16 - 28 + 9 =1628+9=3 = 16 - 28 + 9 = -3

Therefore, the value of (gf)(2)(g \circ f)(2) is 3-3.

This problem has been solved

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