Question

Find the inverse of f(x) = 3x+12

Answer 1

• 
  `\bold{y=(x)/(3)-4}`

Solution:

Hi, let's find the inverse of
`\bold{f(x)=3x+12}`.

We can do it in three easy steps, which are shown below ↓↓↓

• Replace
  `\bold{f(x)}` with
  `\bold{y}`.

`\bold{f(x)=3x+12}`

`\bold{y=3x+12}`

• Interchange the x's and y's.

`\bold{y=3x+12}`

`\bold{x=3y+12}`

• Solve for y.

`\bold{x-12=3y}`

`\bold{3y=x-12}`

`\bold{y=(3x)/(3)-(12)/(3)}`

`\bold{y=(x)/(3) -4}`

Problem solved. It's been a pleasure helping you. ^^

Answer 2

`f^(-1)(x)\text{ = }(x)/(3)\text{ - 4}`

Step-by-step explanation

We want to find the inverse of:

f(x) = 3x + 12

To do this, first replace f(x) with y:

=> y = 3x + 12

Now, make x the subject of the formula:

y - 12 = 3x

`\begin{gathered} \Rightarrow\text{ x = }(y)/(3)\text{ - }(12)/(3) \\ x\text{ = }(y)/(3)\text{ - 4} \end{gathered}`

Now, replace the x with f-1(x) and replace the y with x:

`f^(-1)(x)\text{ = }(x)/(3)\text{ - 4}`