Answer
a. $h(12)=6$
b. $x=33$
c. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$h(x)=-\frac{2}{3}x+14$
a.
Substitute $x=12$ into the function.
$\Rightarrow h(12)=-\frac{2}{3}(12)+14$
Clear the parentheses.
$\Rightarrow h(12)=-8+14$
Subtract.
$\Rightarrow h(12)=6$.
b.
Substitute $h(x)=-8$ into the function.
$\Rightarrow -8=-\frac{2}{3}x+14$
Subtract $14$ from both sides.
$\Rightarrow -8-14=-\frac{2}{3}x+14-14$
Simplify.
$\Rightarrow -22=-\frac{2}{3}x$
Multiply both sides by $-\frac{3}{2}$.
$\Rightarrow -\frac{3}{2}(-22)=-\frac{3}{2}\left (-\frac{2}{3}x \right )$
Simplify.
$\Rightarrow 33=x$.
c.
This is a linear function.
Hence, all real number inputs will result in real number outputs.
The domain is $(-\infty,\infty)$.
and the range is $(-\infty,\infty)$.
