Question

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

Answer 1

Answer:

The inverse is 1/2x +3

Step-by-step 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

Answer 2

Answer:

${f}^{ - 1} (x) = \frac{x + 6}{2}$

Step-by-step 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

$\frac{2y}{2} = \frac{x + 6}{2} \\ \\ y = \frac{x + 6}{2}$

We have the final answer as

${f}^{ - 1} (x) = \frac{x + 6}{2}$

Hope this helps you