Properties and Attributes of Function

Question

What is the domain of the function

f(x)=2x+3

when the range is {3, 5, 9}

please explain how! I really wanna know.

Answer 1

See in the question.

The range contains only 3 values and by observing the function gives only 1 output on one value of x so we can conclude that the function is one-one.

The range is elemental.

So we can calculate the inverse of the funtion.

y=2x+3

x=(y-3)/2 is the inverse.

so one by one we can put the values of y to calculate the values of x which is our domain..

y=3;

x = (3-3)/2; x=0.

y=5

x=(5-3)/2; x=1

y=9

x=(9-3)/2; x=3

Thus, domain is {0, 1, 3}

Answer 2

{3, 5, 9} is your range, so they are the y values. Plug in each of them to get the corresponding x value.

3 = 2x + 3 ---------> x=0

5 = 2x + 3 -----------> x=1

9 = 2x + 3 -----------> x=3

Thus, domain is {0, 1, 3}