Question

Find the inverse function of f(x) = 5x-4. Show your work.

Answer 1

`(1)/(5) x + (4)/(5) = y`

Explanation:

f(x) = 5x-4

1. First, you want to rewrite the function with x and y

y= 5x-4

2. Then, switch the variables x and y

x= 5y-4

3. Now, solve for y.

x= 5y-4

x+4 = 5y

`(1)/(5) x + (4)/(5) = y` --> This is your inverse.

To check:

You can check this answer by plugging your inverse into your original function. You will know that your inverse is correct if your answer is x = 1

1. y= 5x-4,
`y = (1)/(5) x + (4)/(5)`

2. Since they both equal to y, pick one equation to plug into the other. In this case, you are simply setting them equal to each other.

5x-4 =
`(1)/(5) x +(4)/(5)`

3. Solve for x.

5x-4 =
`(1)/(5) x +(4)/(5)`

`(4)/(5)+4 = 5x - (1)/(5)`

24=24x

x=1

4. Since you reached the answer x=1, you didn't get any extraneous solutions and your answer is therefore correct.

Answer 2

The inverse is (x+4)/5

Explanation:

f(x) = 5x-4

Let f(x) =y

y = 5x-4

Exchange x and y

x =5y-4

Solve for y

Add 4 to each to each side

x+4 = 5y-4+4

x+4 = 5y

Divide each side by 5

(x+4)/5 = 5y/5

(x+4)/5 =y

The inverse is (x+4)/5