Express your answer as a polynomial in standard form.

Question

f, of, x, equals, 5, x, minus, 4
f(x)=
5x−4
g, of, x, equals, x, squared, minus, 3, x, minus, 11
g(x)=
x
2
−3x−11
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:

• \(f(x) = 5x - 4\)
• \(g(x) = x^2 - 3x - 11\)

So we need to compute:

\[ f(g(x)) = f(x^2 - 3x - 11) \]

Now we will substitute \(x^2 - 3x - 11\) into \(f(x)\):

\[ f(x^2 - 3x - 11) = 5(x^2 - 3x - 11) - 4 \]

Now we distribute the 5:

\[ = 5x^2 - 15x - 55 - 4 \]

Combine the constant terms:

\[ = 5x^2 - 15x - 59 \]

Now, writing this in standard form, we get:

\[ (f \circ g)(x) = 5x^2 - 15x - 59 \]

Thus, the final answer is:

\[ \boxed{5x^2 - 15x - 59} \]