For each part of this problem, there is no partial credit.

$($a$)$ Find the domain of $f(x)=\frac{\sqrt[\phantom{2}]{x+8}}{e^2-e^x}.$ Write your answer using interval notation.

$f(x)=\frac{\sqrt[\phantom{2}]{x+8}}{e^2-e^x}*\sqrt[\phantom{2}]{x+8}=\frac{(\sqrt[\phantom{2}]{x+8})(\sqrt[\phantom{2}]{x+8})}{e^2-e^x(\sqrt[\phantom{2}]{x+8})}=f(x)=\sqrt[\phantom{2}]{x+8}$

$($b$)$ Find an equation of the line in the $xy-$plane through the points $(-1,3)$ and $(5,-9).$

$x_2-y_1=m(x_2-x_1)$ equation $of$ line: $y=3x+b$

$9-3=m(5-(-1))=\frac{-12}{-4}=\frac{m(4)}{4},m=3$

$=\frac{42-41}{x_2-x_1}\frac{-9-3}{5-(-1)}=\frac{-12}{-4}=3$

$y=mx+b,y=3x+b$

$($c$)$ Let $g(x)=\frac{12}{x}-5.$ Suppose $h0$ and fully simplify the diferente yuvur....