Question

How to find the inverse for f(x) = 2x-6

Answer 1

`{f}^( - 1) (x) = (x + 6)/(2) \\`

Explanation:

`f(x) = 2x-6`

To find the inverse of f(x) , equate f(x) to y that's

`y = 2x - 6`

Next interchange the terms that's x becomes y and y becomes x

`x = 2y - 6`

Next solve for y

Move 6 to the other side of the equation

That's

`2y = x + 6`

Divide both sides by 2 to make y stand alone

`(2y)/(2) = (x + 6)/(2) \\ \\ y = (x + 6)/(2)`

We have the final answer as

`{f}^( - 1) (x) = (x + 6)/(2) \\`

Hope this helps you

Answer 2

The inverse is 1/2x +3

Explanation:

f(x) = 2x-6

Replace f(x) with y

y= 2x-6

Exchange x and y

x = 2y-6

Solve for y

Add 6 to each side

x+6 = 2y-6+6

x+6 = 2y

Divide each side by 2

(x+6)/2 = 2y/2

1/2 x+3 = y

The inverse is 1/2x +3