Question

What is the inverse of the function f(x) = 1/4x-12?

Answer 1

`\huge\boxed{f^(-1)(x)=4x+48}`

Explanation:

In order to find the inverse of a function, we need to follow a couple of steps.

• Step 1: Write the function as
  `y=mx+b`
• Step 2: Swap all x and y values
• Step 3: Solve for y
• Step 4: Replace y with
  `f^(-1)(x)`

We can follow these steps to find the inverse of this function.

Step 1: We can just replace the f(x) with y, making our function
`y=(1)/(4)x-12`.

Step 2: We can swap where the x and y values are, making our equation

`x = (1)/(4)y-12`

Step 3: We can now solve for y.

• 
  `x = (1)/(4)y-12`
• 
  `x + 12 = (1)/(4)x`
• 
  `4x+48 =y`

We now have the function as
`y = 4x+48`.

Step 4: We can now replace the y with
`f^(-1)(x)`.

`f^(-1)(x) =4x+48`

Therefore the inverse of
`f(x) = (1)/(4)x-12` is
`f^(-1)(x) =4x+48`.

Hope this helped!