Express your answer as a polynomial in standard form.

Question

f, of, x, equals, x, minus, 4
f(x)=
x−4
g, of, x, equals, 2, x, squared, plus, 2, x, plus, 14
g(x)=
2x
2
+2x+14
Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesis
Find: (f∘g)(x)

Answer 1

To find \((f \circ g)(x)\) or \(f(g(x))\), we need to substitute \(g(x)\) into \(f(x)\).

Given:

\[ f(x) = x - 4 \] \[ g(x) = 2x^2 + 2x + 14 \]

Now, we substitute \(g(x)\) into \(f\):

\[ (f \circ g)(x) = f(g(x)) = f(2x^2 + 2x + 14) \]

Now, using the expression for \(f(x)\):

\[ f(2x^2 + 2x + 14) = (2x^2 + 2x + 14) - 4 \]

Now, simplify the expression:

\[ = 2x^2 + 2x + 14 - 4 \] \[ = 2x^2 + 2x + 10 \]

So, the final expression for \((f \circ g)(x)\) in standard polynomial form is:

\[ (f \circ g)(x) = 2x^2 + 2x + 10 \]