Answer
a. $f(30)=10$
b. $f(-19)=--1215$
c. $x=20$
d. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$f(x)=25x-740$
a.
Substitute $x=30$ into the function.
$\Rightarrow f(30)=25(30)-740$
Clear the parentheses.
$\Rightarrow f(30)=750-740$
Subtract.
$\Rightarrow f(30)=10$.
b.
Substitute $x=-19$ into the function.
$\Rightarrow f(-19)=25(-19)-740$
Clear the parentheses.
$\Rightarrow f(-19)=-475-740$
Add like terms.
$\Rightarrow f(-19)=-1215$.
c.
Substitute $f(x)=-240$ into the function.
$\Rightarrow -240=25x-740$
Add $740$ to both sides.
$\Rightarrow -240+740=25x-740+740$
Simplify.
$\Rightarrow 500=25x$
Divide both sides by $25$.
$\Rightarrow \frac{500}{25}=\frac{25x}{25}$
Simplify.
$\Rightarrow 20=x$.
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 $(-\infty,\infty)$.
