Answer
a. $f(4)=25$
b. $x=-4$
c. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$f(x)=7x-3$
a.
Substitute $x=4$ into the function.
$\Rightarrow f(4)=7(4)-3$
Clear the parentheses.
$\Rightarrow f(4)=28-3$
Subtract.
$\Rightarrow f(4)=25$.
b.
Substitute $f(x)=-31$ into the function.
$\Rightarrow -31=7x-3$
Add $3$ to both sides.
$\Rightarrow -31+3=7x-3+3$
Simplify.
$\Rightarrow -28=7x$
Divide both sides by $7$.
$\Rightarrow \frac{-28}{7}=\frac{7x}{7}$
Simplify.
$\Rightarrow -4=x$.
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 $(-\infty,\infty)$.