College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 10

If $f(x) = 4 - \sqrt{3x-6}$, find $f(5), \quad f(9), \quad f(a + 2), \quad f(-x), \quad f(x^2)$ and $[f(x)]^2$

$
\begin{equation}
\begin{aligned}
f(5) &= 4 -\sqrt{3(5) - 6} &&& f(9) &= 4 - \sqrt{3(9) - 6}\\
\\
&= 1 &&& &= 4 - \sqrt{21}
\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}
f(a+2) &= 4- \sqrt{3 (a + 2) - 6} &&& f(-x) &= 4- \sqrt{3(-x)-6}\\
\\
&= 4- \sqrt{3a + 6 - 6} &&& &= 4 - \sqrt{-3x - 6}\\
\\
&= 4- \sqrt{3a}
\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}
f(x^2) &= 4 - \sqrt{3(x^2) - 6} &&& [f(x)]^2 &= (4- \sqrt{3x-6})^2\\
\\
&= 4- \sqrt{3x^2 - 6} &&& &= 16 - 8 \sqrt{3x-6} + 3x-6\\
\\
&= 4- \sqrt{3(x^2 -2)} &&& &= 3x - 8 \sqrt{3x-6} + 10
\end{aligned}
\end{equation}
$