# What is the domain of f(x)=3x+2 when the range is {-2, -1, 2}?

Sep 19, 2015

$\left\{- \frac{4}{3} , - 1 , 0\right\}$

#### Explanation:

This is a straight line graph of gradient 3 and y-intercept 2.

However, if the range only consists of the 3 points given, then the domain will also only consist of the corresponding inverse images of these 3 points.

By definition, $y = {f}^{- 1} \left(x\right) \iff f \left(y\right) = x$

Hence in this case, ${f}^{- 1} \left(x\right) = \frac{y - 2}{3}$

Therefore the domain is $\left\{- \frac{4}{3} , - 1 , 0\right\}$

The full graph is drawn below, but under the restrictions of the question, you should delete all values except the 3 given.

graph{3x+2 [-11.25, 11.25, -5.62, 5.62]}