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
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
If we have a function, we can find its inverse if we do the
following-:
[tex]\tiny\bullet[/tex] replace f(x) with y.
[tex]\boldsymbol{\sf{y=\displaystyle\frac{1}{9}x+2}}[/tex]
[tex]\tiny\bullet[/tex] switch the places of x and y
[tex]\boldsymbol{\sf{x=\displaystyle\frac{1}{9}y+2}}}[/tex]
[tex]\bullet[/tex] solve for y
[tex]\boldsymbol{\sf{x\times9=\frac{1}{9}y\times9+2\times9}}[/tex]
[tex]\boldsymbol{\sf{9x=y+18}}[/tex]
[tex]\boldsymbol{\sf{-y=-9x+18}}[/tex]
[tex]\boldsymbol{\sf{y=9x-18}}}[/tex]
[tex]\boldsymbol{\sf{f(x)^{-1}=9x+18}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
