Answer
a. $h(105)=1970$
b. $x= -\frac{320}{7}$
c. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$h(x)=14x+500$
a.
Substitute $x=105$ into the function.
$\Rightarrow h(105)=14(105)+500$
Clear the parentheses.
$\Rightarrow h(105)=1470+500$
Add.
$\Rightarrow h(105)=1970$.
b.
Substitute $h(x)=-140$ into the function.
$\Rightarrow -140=14x+500$
Subtract $500$ from both sides.
$\Rightarrow -140-500=14x+500-500$
Simplify.
$\Rightarrow -640=14x$
Divide both sides by $14$.
$\Rightarrow \frac{-640}{14}={14x}{14}$
Simplify.
$\Rightarrow -\frac{320}{7}=x$.
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 $(-\infty,\infty)$.
