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

1 Answer
Sep 19, 2015

#{-4/3,-1, 0}#


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)(x)ifff(y)=x#

Hence in this case, #f^(-1)(x)=(y-2)/3#

Therefore the domain is #{-4/3,-1, 0}#

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]}