Question

Express your answer as a polynomial in standard form.
f, of, x, equals, 3, x, plus, 14
f(x)=
3x+14
g, of, x, equals, 2, x, squared, minus, 4, x, plus, 1
g(x)=
2x
2
−4x+1
Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesis
Find: (f∘g)(x)

Answer 1

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

Given:

- \(f(x) = 3x + 14\)
- \(g(x) = 2x^2 - 4x + 1\)

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

\[
f(g(x)) = f(2x^2 - 4x + 1)
\]

Now, replace \(x\) in \(f(x)\) with \(g(x)\):

\[
f(g(x)) = 3(2x^2 - 4x + 1) + 14
\]

Now, distribute \(3\):

\[
= 3 \cdot 2x^2 - 3 \cdot 4x + 3 \cdot 1 + 14
\]
\[
= 6x^2 - 12x + 3 + 14
\]

Now combine like terms:

\[
= 6x^2 - 12x + 17
\]

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

\[
\boxed{6x^2 - 12x + 17}
\]