The functions $f, g$, and $h$ are defined as follows.
\[
f(x)=|12 x-13| \quad g(x)=\sqrt{13+5 x} \quad h(x)=\frac{x^{3}+2}{x^{3}}
\]
Find $f\left(-\frac{3}{4}\right), g(2)$, and $h(-4)$
Simplify your answers as much as possible.
\[
\begin{array}{r}
f\left(-\frac{3}{4}\right)=\square \\
g(2)=\square \\
h(-4)=\square
\end{array}
\]
Answer
So, the final answers are $f\left(-\frac{3}{4}\right)=\boxed{22}$, $g(2)=\boxed{\sqrt{23}}$, and $h(-4)=\boxed{\frac{31}{32}}$.
Step 1 ：Define the functions $f, g, h$ as $f(x)=|12 x-13|$, $g(x)=\sqrt{13+5 x}$, and $h(x)=\frac{x^{3}+2}{x^{3}}$ respectively.
Step 2 ：Substitute $x=-\frac{3}{4}$ into $f(x)$ to get $f\left(-\frac{3}{4}\right)=|12(-\frac{3}{4})-13|=22$.
Step 3 ：Substitute $x=2$ into $g(x)$ to get $g(2)=\sqrt{13+5(2)}=\sqrt{23}$.
Step 4 ：Substitute $x=-4$ into $h(x)$ to get $h(-4)=\frac{(-4)^{3}+2}{(-4)^{3}}=\frac{31}{32}$.
Step 5 ：So, the final answers are $f\left(-\frac{3}{4}\right)=\boxed{22}$, $g(2)=\boxed{\sqrt{23}}$, and $h(-4)=\boxed{\frac{31}{32}}$.
