Question

Which function is the inverse of

Answer 1

Given:-

• 
  `(18x+7)/(3)` .

To find:-

• The inverse of this function.

Answer:-

Let us take that ;

`\implies y = (18x+7)/(3) \\`

Now to find inverse, interchange x and y .

`\implies x = (18y+7)/(3) \\`

Now solve for y ,

`\implies 3x = 18y + 7\\`

Flip the sides,

`\implies 18y + 7 = 3x \\`

Subtract 7 on both sides,

`\implies 18y = 3x - 7 \\`

Divide both the sides by 18,

`\implies y =(3x-7)/(18) \\`

Finally substitute
`y =f^(-1)(x)`

`\implies \underline{\underline{ f^(-1)(x) = (3x-7)/(18)}}\\`

This is our required answer.

and we are done!

Answer 2

`(3x-7)/(18)`

Explanation:

let y equal the expression, then rearrange making x the subject.

y =
`(18x+7)/(3)` ( multiply both sides by 3 )

3y = 18x + 7 ( subtract 7 from both sides )

3y - 7 = 18x ( isolate x by dividing both sides by 18 )

`(3y-7)/(18)` = x

change y back into terms of x with x being the inverse, that is

`(3x-7)/(18)` ← is the inverse