Express your answer as a polynomial in standard form.

Question

f, of, x, equals, minus, 5, x, plus, 12
f(x)=
−5x+12
g, of, x, equals, x, squared, plus, 7, x, plus, 1
g(x)=
x
2
+7x+1
Find: , f, of, g, of, x
Find: f(g(x))

Answer 1

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

Given:

• \( f(x) = -5x + 12 \)
• \( g(x) = x^2 + 7x + 1 \)

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

\[ f(g(x)) = f(x^2 + 7x + 1) \]

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

\[ f(g(x)) = -5(g(x)) + 12 \]

Substituting \( g(x) \) into the equation:

\[ f(g(x)) = -5(x^2 + 7x + 1) + 12 \]

Distributing \(-5\):

\[ f(g(x)) = -5x^2 - 35x - 5 + 12 \]

Now, combine the constant terms:

\[ f(g(x)) = -5x^2 - 35x + 7 \]

Thus, in standard form, we can express \( f(g(x)) \) as:

\[ f(g(x)) = -5x^2 - 35x + 7 \]