The inverse of the function is [tex]f^{-1}x= \sqrt{\frac{x-4}{3} } + 2[/tex]
Given the function
[tex]f(x) = 3(x - 2)^2 + 4[/tex]
To get the inverse, you will follow the same step as shown:
Rewrite the equation to have:
[tex]y= 3(x - 2)^2 + 4[/tex]
Replace x with y
[tex]x = 3(y - 2)^2 + 4[/tex]
[tex]x = 3(y - 2)^2 + 4\\x-4=3(y - 2)^2\\\frac{x-4}{3} = (y-2)^2\\ y-2=\sqrt{\frac{x-4}{3} } \\y = \sqrt{\frac{x-4}{3} } + 2[/tex]
Hence the inverse of the function is [tex]f^{-1}x= \sqrt{\frac{x-4}{3} } + 2[/tex]
Learn more on inverse of a function here: https://brainly.com/question/2873333
