Question

Find the inverse of f(x)=−3/2x+7/2.

Answer 1

Answer:
`f^(-1)(x)=-(2)/(3)x+(7)/(3)`

Explanation:

To find the inverse of a function, you want to replace x with y and y with x. Then, you solve for y.

`y=-(3)/(2)x+(7)/(2)` [replace y with x and x with y]

`x=-(3)/(2)y+(7)/(2)` [subtract both sides by 7/2]

`x-(7)/(2) =-(3)/(2)y` [multiply both sides by -2/3]

`-(2)/(3) (x-(7)/(2) )=y` [distribute]

`y=-(2)/(3)x+(7)/(3)`

Now, we have our inverse function.

`f^-^1(x)=-(2)/(3)x+(7)/(3)`