Question

Which of the following is the inverse of F(x)

Answer 1

to solve for the inverse

1. replace f(x) with y
2. switch x and y
3. solve for y
4. replace y with f⁻¹(x)



so

`f(x)=(2x-3)/(5)`
replace f(x) with y

`y=(2x-3)/(5)`
switch x and y

`x=(2y-3)/(5)`
times both sides by 5

`5x=2y-3`
add 3 to both sides

`5x+3=2y`
divide by 2

`(5x+3)/(2)=y`

`y=(5x+3)/(2)`
repace y with f⁻¹(x)

`f^(-1)(x)=(5x+3)/(2)`

D is the answer