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, 3, right parenthesis, .(g∘f)(3).

Question

f, of, x, equals, 3, x, minus, 9
f(x)=
3x−9
g, of, x, equals, 3, x, squared, minus, 5, x, plus, 15
g(x)=
3x
2
−5x+15

Answer 1

To find \((g \circ f)(3)\), we first need to calculate \(f(3)\) and then use that result as the input for \(g\).

1. Calculate \(f(3)\): \[ f(x) = 3x - 9 \] \[ f(3) = 3(3) - 9 = 9 - 9 = 0 \]

2. Calculate \(g(f(3))\) which is \(g(0)\): \[ g(x) = 3x^2 - 5x + 15 \] Substitute \(x = 0\): \[ g(0) = 3(0)^2 - 5(0) + 15 = 0 - 0 + 15 = 15 \]

Now we combine the results from the two calculations:

\[ (g \circ f)(3) = g(f(3)) = g(0) = 15 \]

Thus, the value of \((g \circ f)(3)\) is \(\boxed{15}\).