Question

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

Answer 1

f - 1 is the answer because f - 1x take the one away and f - x is all there's left

Answer 2

`f^(-1)(x)`=
`(1)/(4x-12))`.

Explanation:

Given : f(x) =
`(1)/(4x)+3`.

To find : inverse

Solution : We have given f(x) =
`(1)/(4x)+3`.

Step 1: f(x) = y

y =
`(1)/(4x)+3`.

Step 2: replace x and y .

x =
`(1)/(4y)+3`.

Step 3:

Solve for y

On subtracting both sides by 3

x -3 =
`(1)/(4y)`.

Taking reciprocal both sides

4y =
`(1)/(x-3)`.

On dividing both sides by 4

y =
`(1)/(4(x-3))`.

Take
`f^(-1)(x)=y`.

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

Therefore,
`f^(-1)(x)`=
`(1)/(4x-12)`.