Answer
a. $f(20)=\frac{23}{5}$
b. $f(12)=3$
c. $x=47$
d. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$f(x)=\frac{1}{5}x+\frac{3}{5}$
a.
Substitute $x=20$ into the function.
$\Rightarrow f(20)=\frac{1}{5}(20)+\frac{3}{5}$
Clear the parentheses.
$\Rightarrow f(20)=\frac{20}{5}+\frac{3}{5}$
Add numerators because denominators are same.
$\Rightarrow f(20)=\frac{23}{5}$.
b.
Substitute $x=12$ into the function.
$\Rightarrow f(12)=\frac{1}{5}(12)+\frac{3}{5}$
Clear the parentheses.
$\Rightarrow f(12)=\frac{12}{5}+\frac{3}{5}$
Add numerators because denominators are same.
$\Rightarrow f(12)=\frac{15}{5}$.
Simplify.
$\Rightarrow f(12)=3$.
c.
Substitute $f(x)=10$ into the function.
$\Rightarrow 10=\frac{1}{5}x+\frac{3}{5}$
Multiply the equation by $5$.
$\Rightarrow 5(10)=5\left (\frac{1}{5}x+\frac{3}{5}\right )$
Use distributive property.
$\Rightarrow 5(10)=5\left (\frac{1}{5}x\right )+5\left (\frac{3}{5}\right )$
Simplify.
$\Rightarrow 50=x+3$
Subtract $3$ from both sides.
$\Rightarrow 50-3=x+3-3$
Simplify.
$\Rightarrow 47=x$.
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 $(-\infty,\infty)$.
