Question

for the function $f(x)=\sqrt{2 - x}$, find each of the following
(a) $f(p)$
$f(p)=\sqrt{2 - p}$ (simplify your answer.)
(b) $f(-r)$
$f(-r)=\sqrt{2 + r}$ (simplify your answer)
(c) $f(m + 4)$
$f(m + 4)=\square$ (simplify your answer)

Explanation:

Step1: Substitute x with m+4

To find \( f(m + 4) \), we substitute \( x = m + 4 \) into the function \( f(x)=\sqrt{2 - x} \).
So we get \( f(m + 4)=\sqrt{2-(m + 4)} \).

Step2: Simplify the expression inside the square root

Simplify \( 2-(m + 4) \):
\( 2-(m + 4)=2 - m - 4=-m - 2 \)
So \( f(m + 4)=\sqrt{-m - 2} \)

Answer:

\( \sqrt{-m - 2} \)