Question

If the function is given by $g\left(x\right)=\frac{2}{3}x+7$, then the domain value that corresponds to a range value of $3$ is

• A. $-6$
• B. $-2$
• C. $6$
• D. $9$

Answer 1

The correct option is A $-6$

Given, $g\left(x\right)=\frac{2}{3}x+7,g\left(x\right)=3$
$\Rightarrow 3=\frac{2}{3}x+7$
$\Rightarrow 9-21=2x$
$\Rightarrow -12=2x$
$\Rightarrow x=-6$
You could also graph the function and find the value of $x$ (the domain value) for which the value of $y$ (the range value) is $3$. The point on the graph is $(-6,3)$.
Therefore the domain value is $-6$.