Question

If f(x)=5x-3 which expression represents its inverse function?

Answer 1

f⁻¹(x) = x+3 / 5

Explanation:

We have given a function.

f(x) = 5x-3

We have to find the inverse of given function.

Step 1. Put y = f(x) in given function

y = 5x-3

Step 2. Add 3 to both sides of above equation

y+3 = 5x-3+3

y+3 = 5x

Step 3.Divide by 5 to both sides of above equation

y+3 / 5 = 5x / 5

y+3 / 5 = x

Step 4. Swap sides

x = y+3 / 5

Step 5.Put x = f⁻¹(y) in above equation

f⁻¹(y) = y+3 / 5

Step 6. Replace x with y

f⁻¹(x) = x+3 / 5 is the inverse of f(x) = 5x-3.

Answer 2

`f^(-1) (x)  =`
`(1)/(5)(x+3)`

Explanation:

In order to find the inverse of a function we need to follow the given step

We shall do step by step to find the inverse of given function

Step(1) : we write f(x) =y

therefore here y =5x-3

Step(2) Interchanging x and y

x =5y-3

or

5y-3 = x

Step :solving the obtained equation for y

5y = x+3

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

`f^(-1) (x)  =`
`(1)/(5)(x+3)`