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, minus, 3, right parenthesis, .(g∘f)(−3).

Question

f, of, x, equals, x, squared, plus, 5, x, plus, 9
f(x)=
x
2
+5x+9
g, of, x, equals, 4, x, minus, 10
g(x)=
4x−10

Answer 1

To find \((g \circ f)(-3)\), we first need to evaluate \(f(-3)\) and then use this result to evaluate \(g\).

1. Calculate \(f(-3)\): \[ f(x) = x^2 + 5x + 9 \] Substituting \(-3\) for \(x\): \[ f(-3) = (-3)^2 + 5(-3) + 9 \] Calculating each term: \[ = 9 - 15 + 9 \] \[ = 9 - 15 + 9 = 3 \]

2. Now calculate \(g(f(-3)) = g(3)\): \[ g(x) = 4x - 10 \] Substituting \(3\) for \(x\): \[ g(3) = 4(3) - 10 \] \[ = 12 - 10 = 2 \]

Thus, the value of \((g \circ f)(-3)\) is: \[ \boxed{2} \]