Question

What is the inverse of the function f(x) = 1/9x+2

Answer 1

`\frak{Hi!}`

`\orange\hspace{300pt}\above3`

If we have a function, we can find its inverse if we do the

following-:

`\tiny\bullet` replace f(x) with y.

`\boldsymbol{\sf{y=\displaystyle(1)/(9)x+2}}`

`\tiny\bullet` switch the places of x and y

`\boldsymbol{\sf{x=\displaystyle(1)/(9)y+2}}}`

`\bullet` solve for y

`\boldsymbol{\sf{x*9=(1)/(9)y*9+2*9}}`

`\boldsymbol{\sf{9x=y+18}}`

`\boldsymbol{\sf{-y=-9x+18}}`

`\boldsymbol{\sf{y=9x-18}}}`

`\boldsymbol{\sf{f(x)^(-1)=9x+18}}`

`\orange\hspace{300pt}\above3`

Answer 2

Hello,

f(x) = 1/9x + 2 ⇔ y = 1/9x + 2 ⇔ 1/9x = y - 2 ⇔ x = 9(y - 2)

x = 9y - 18

⇒ f⁻¹(x) = 9x - 18