Question

Given that f, of, x, equals, x, squared, plus, 7, x, plus, 10f(x)=x
2
+7x+10 and g, of, x, equals, x, plus, 5g(x)=x+5, find left parenthesis, f, plus, g, right parenthesis, left parenthesis, x, right parenthesis(f+g)(x) and express the result as a polynomial in simplest form.

Answer 1

To find \( (f + g)(x) \), we need to add the functions \( f(x) \) and \( g(x) \).

Given:
\[
f(x) = x^2 + 7x + 10
\]
\[
g(x) = x + 5
\]

Now, we can find \( (f + g)(x) \) by adding \( f(x) \) and \( g(x) \):

\[
(f + g)(x) = f(x) + g(x)
\]
\[
= (x^2 + 7x + 10) + (x + 5)
\]

Now, let's combine like terms:

1. Combine \( x^2 \) terms: \( x^2 \)
2. Combine \( x \) terms: \( 7x + x = 8x \)
3. Combine constant terms: \( 10 + 5 = 15 \)

Putting it all together, we get:

\[
(f + g)(x) = x^2 + 8x + 15
\]

Thus, the result expressed as a polynomial in simplest form is:

\[
\boxed{x^2 + 8x + 15}
\]