If (x+3)/(4), what is the equation for f–1(x)?

Question

If
`(x+3)/(4)`, what is the equation for f–1(x)?

Answer 1

4x-3 is the inverse of given function.

Explanation:

Given function is

f(x) = x+3 / 4

Putting y = f(x) in above equation, we have

y = x+3 / 4

We have to separate x from above equation.

Multiplying 4 by above equation, we have

4y = 4(x+3 / 4)

4y = x+3

Adding -3 to both sides of above equation, we have

4y-3 = x+3-3

4y-3 = x

Swapping above equation, we have

x = 4y-3

Putting x = f⁻¹(y) in above equation , we have

f⁻¹(y) = 4y-3

Replacing y with x in above equation, we have

f⁻¹(x) = 4x-3 which is the answer.

Answer 2

`f^(-1)(x) = 4x-3` is the right answer.

Explanation:

I the function is
`f(x) = (x+3)/(4)`

`f(x)=(1)/(4)(x+3)`

Then we have to find inverse of function f(x).

we will write the equation as
`y=(1)/(4)(x+3)`

4y = x + 3

x = 4y - 3

Now we will rewrite the function as

`f^(-1)(x) = 4x-3`

So the answer is
`f^(-1)(x) = 4x-3`