Answer
a. $g(15)=-69.5$
b. $g(-20)=81$
c. $x=\frac{406}{43}$
d. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$g(x)=-4.3x-5$
a.
Substitute $x=15$ into the function.
$\Rightarrow g(15)=-4.3(15)-5$
Clear the parentheses.
$\Rightarrow g(15)=-64.5-5$
Subtract.
$\Rightarrow g(15)=-69.5$.
b.
Substitute $x=-20$ into the function.
$\Rightarrow g(-20)=-4.3(-20)-5$
Clear the parentheses.
$\Rightarrow g(-20)=86-5$
Add like terms.
$\Rightarrow g(-20)=81$.
c.
Substitute $g(x)=-45.6$ into the function.
$\Rightarrow -45.6=-4.3x-5$
Add $5$ to both sides.
$\Rightarrow -45.6+5=-4.3x-5+5$
Simplify.
$\Rightarrow -40.6=-4.3x$
Divide both sides by $-4.3$.
$\Rightarrow \frac{-40.6}{-4.3}=\frac{-4.3x}{-4.3}$
Simplify.
$\Rightarrow \frac{406}{43}=x$.
d.
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 $(-\infty,\infty)$.
