Question

hw 2.8 algebra of functions and function compositions
question 14 of 17 (2 points) | question attempt: 1 of unlimited
given the function defined by ( g(x) = -x^2 - 4x + 2 ), find ( g(-pi) ). write your answer in exact, simplified form.
your answer
( g(-pi) = )

Explanation:

Step1: Substitute \( x = -\pi \) into \( g(x) \)

We have the function \( g(x) = -x^2 - 4x + 2 \). Substitute \( x = -\pi \) into the function:
\( g(-\pi) = -(-\pi)^2 - 4(-\pi) + 2 \)

Step2: Simplify each term

First, simplify \( -(-\pi)^2 \). Since \( (-\pi)^2=\pi^2 \), so \( -(-\pi)^2 = -\pi^2 \).
Next, simplify \( - 4(-\pi)=4\pi \).
The constant term is \( +2 \).

Step3: Combine the terms

Combine the simplified terms: \( g(-\pi)=-\pi^2 + 4\pi + 2 \)

Answer:

\(-\pi^2 + 4\pi + 2\)