Question

Inverse of f(x) = 2x – 4.

Answer 1

Answer: x/2 + 2 = y

Explanation:

Our task is to find the inverse of the following function:

`\sf{f(x)=2x-4}`

To find the inverse of any function, we follow these steps:

• Replace f(x) with y.
• Switch the x's and y's.
• Solve for y.

Step one:

`\sf{y=2x-4}`

Step two:

`\sf{x=2y-4}`

Step three:

`\sf{x=2y-4}`

`\sf{x+4=2y}`

`\sf{\cfrac{x+4}{2}=y}`

Simplify:

`\sf{\cfrac{x}{2}+\cfrac{4}{2}=y}`

`\sf{\cfrac{x}{2}+2=y}`

Therefore, our answer is x/2 + 2 = y.

We're done ^_^

Answer 2

Answer:
`f^(-1)(x)=(1)/(2) x+2`

Explanation:

To find the inverse, we flip y and x, then solve for y again.

Given:

f(x) = 2x – 4

Change to y:

y = 2x – 4

Flip x and y:

x = 2y – 4

Add 4 to both sides of the equation:

x + 4 = 2y

Reflexive property:

2y = x + 4

Divide both sides of the equation by 2:

y =
`(1)/(2)`x + 2

Rewrite as the inverse:

`f^(-1)(x)=(1)/(2) x+2`