Question

If g(x) = 3x + 5, what is g^–1(x)?

Answer 1

To find the inverse, you need to "undo" the actions of the original function.

eg, g(4) = 3*4 + 5 = 17. How do you get from 17 back to 4?

first, you would want to subtract 5, leaving 12. Then you can divide by 3.

Thus, \[g^{-1}(x) = 1/3(x-5)\]

Answer 2

g(x)=3x+5
rewrite as y=3x+5
step 1: switch x and y
x=3y+5
Step 2: solve for y
x=3y+5
x-5=3y
(x-5)/3=y
(1/3)x-(5/3)=y^-1

Answer 3

Note that both answers given are the same, just different variation