the inverse of a function
steps to find the inverse of a function
step 1: replace f(x) with y
step 2: replace all x's with y's and y's with x's
step 3: solve for y
step 4: replace y with [tex]f^{-1}(x)[/tex], the ineverse of f(x) or whatever function name
given [tex]f(x)=9x^2-12[/tex]
step 1: replace f(x) with y
[tex]y=9x^2-12[/tex]
step 2: replace all x's with y's and y's with x's
[tex]x=9y^2-12[/tex]
step 3: solve for y
[tex]x=9y^2-12[/tex]
[tex]x+12=9y^2[/tex]
[tex]\frac{x+12}{9}=y^2[/tex]
[tex]\sqrt{\pm \frac{x+12}{9}}=y[/tex]
[tex]y=\frac{\pm \sqrt{x+12}}{3}[/tex]
step 4: replace y with function name
here's where we just match which one matches [tex]inverse=\frac{\pm \sqrt{x+12}}{3}[/tex]
that would be A
