If the range of the function f(x) = 4x – 3 is {11.4, 15, 17, 29}, what is its domain?

The range is the y-component of the function

the function looks like it just consists of 4 points which have y-coordinates of 11.4, 15,17, and 29

so in order to find domain (x-component of the function), you just substitute each y value, and find the corresponding x-value

11.4 =4x -3
14.4=4x
x=14.4/4

15=4x-3
18=4x
x= 18/4

etc etc

Range is the output

basically
f(x)=range
just solve for the values of x that make them true

just solve
4x-3=11.4
4x-3=15
4x-3=17
4x-3=29
those values aer the domain

solving each
add 3 to both sides
4x=14.4
4x=18
4x=20
4x=32

divide both sides by 4

x=3.6
x=4.5
x=5
x=8

the domain is D={3.6, 4.5, 5, 8}