Answer
a. $h(35)=26$
b. $x=-\frac{7}{2}$
d. Domain:- $(-\infty,\infty)$. Range:- $(-\infty,\infty)$.
Work Step by Step
The given function is
$h(x)=\frac{4}{7}x+6$
a.
Substitute $x=35$ into the function.
$\Rightarrow h(35)=\frac{4}{7}(35)+6$
Clear the parentheses.
$\Rightarrow h(35)=20+6$
Subtract.
$\Rightarrow h(35)=26$.
b.
Substitute $h(x)=4$ into the function.
$\Rightarrow 4=\frac{4}{7}x+6$
Multiply both sides by $7$.
$\Rightarrow 7(4)=7\left (\frac{4}{7}x+6\right )$
Use distributive property.
$\Rightarrow 7(4)=7\left (\frac{4}{7}x\right )+7\left (6\right )$
Simplify.
$\Rightarrow 28=4x+42$
Subtract $42$ from both sides.
$\Rightarrow 28-42=4x+42-42$
Simplify.
$\Rightarrow -14=4x$
Divide both sides by $4$.
$\Rightarrow \frac{-14}{4}=\frac{4x}{4}$
Simplify.
$\Rightarrow -\frac{7}{2}=x$.
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 $(-\infty,\infty)$.
