Answer
a. $g(3)=27$
b. $g(-7)=-23$
c. $x=7$
d. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$g(x)=5x+12$
a.
Substitute $x=3$ into the function.
$\Rightarrow g(3)=5(3)+12$
Clear the parentheses.
$\Rightarrow g(3)=15+12$
Add.
$\Rightarrow g(3)=27$.
b.
Substitute $x=-7$ into the function.
$\Rightarrow g(-7)=5(-7)+12$
Clear the parentheses.
$\Rightarrow g(-7)=-35+12$
Subtract.
$\Rightarrow g(-7)=-23$.
c.
Substitute $g(x)=47$ into the function.
$\Rightarrow 47=5x+12$
Subtract $12$ from both sides.
$\Rightarrow 47-12=5x+12-12$
Simplify.
$\Rightarrow 35=5x$
Divide both sides by $5$.
$\Rightarrow \frac{35}{5}={5x}{5}$
Simplify.
$\Rightarrow 7=x$.
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 $(-\infty,\infty)$.
