Question

(01.02 LC)

Given f(x) = the quantity of x minus 5, divided by 3, solve for f−1(3). (5 points)


−1
14
18
21

Answer 1

So to find the inverse of this function, replace f(x) with y, switch x and y, then solve for y. This is what it'll look like:
`x=(y-5)/(3)`

Firstly, multiply both sides by 3:
`3x=y-5`

Next, add both sides by 5 and replace y with f^-1 (x) and your inverse equation is:
`3x+5=f^(-1)(x)`

Now that we have the inverse, plug in 3 into it and solve:

`3(3)+5=f^(-1)(3)\\ 9+5=f^(-1)(3)\\ 14=f^(-1)(3)`

In short, the answer is 14, or the second option.