Answer
a. $f(5)=3$
b. $f(-10)=-27$
c. $x=3$
d. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$
Work Step by Step
The given function is
$f(x)=2x-7$
a.
Substitute $x=5$ into the function.
$\Rightarrow f(5)=2(5)-7$
Clear the parentheses.
$\Rightarrow f(5)=10-7$
Subtract.
$\Rightarrow f(5)=3$.
b.
Substitute $x=-10$ into the function.
$\Rightarrow f(-10)=2(-10)-7$
Clear the parentheses.
$\Rightarrow f(-10)=-20-7$
Add like terms.
$\Rightarrow f(-10)=-27$.
c.
Substitute $f(x)=-1$ into the function.
$\Rightarrow -1=2x-7$
Add $7$ to both sides.
$\Rightarrow -1+7=2x-7+7$
Simplify.
$\Rightarrow 6=2x$
Divide both sides by $2$.
$\Rightarrow \frac{6}{2}={2x}{2}$
Simplify.
$\Rightarrow 3=x$.
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 $(-\infty,\infty)$.
