Question

f(x) = x^2 + 1 \quad g(x) = 5 - x

(f + g)(x) =

\bigcirc \quad x^2 + x - 4
\bigcirc \quad x^2 + x + 4
\bigcirc \quad x^2 - x + 6
\bigcirc \quad x^2 + x + 6

Explanation:

Write the definition of function addition

$$ (f + g)(x) = f(x) + g(x) $$

Substitute the given functions

$$ (f + g)(x) = (x^2 + 1) + (5 - x) $$

Simplify and rearrange terms

$$ (f + g)(x) = x^2 - x + 6 $$

Answer:

• (A) \(x^2 + x - 4\)
• (B) \(x^2 + x + 4\)
• (C) \(x^2 - x + 6\) (Correct answer)
• (D) \(x^2 + x + 6\)