Question

What is the inverse of f(x) = 1/3x + 2?

h(x) = 1/3x + 2
h(x) = 1/3x - 2
h(x) = 3x - 2
h(x) = 3x - 6

Answer 1

The inverse is h(x) = 3x - 6

Answer 2

h(x) = 3x -6.

Explanation:

Given :f(x) =
`(1x)/(3) + 2`.

To find : inverse .

Solution : We have given that

f(x) =
`(1x)/(3) + 2`.

Step 1) y =
`(1x)/(3) + 2`.

Step 2) Now, interchange x and y.

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

Step 3:

Solve for y

On subtracting both sides by 2

x -2 =
`(y)/(3)`.

On multiplying both the sides by 3

3 ( x -2) = y

On taking reciprocal

y = 3x -6

This the inverse of f(x) = h(x)

Therefore, h(x) = 3x -6.