### Home > INT3 > Chapter 6 > Lesson 6.3.1 > Problem6-84

6-84.

What is the equation for the inverse of the function f(x) = + 1? Sketch the graph of both the original and the inverse functions. Homework Help ✎

Change f(x) to y. Then interchange the x and y.

$x=2\sqrt{\frac{\left(y-3\right)}{4}}+1$

Subtract 1 from each side, and then square each side to get rid of the square root.

$\left(x-1\right)^2=\left(2\sqrt{\frac{y-3}{4}}\right)^2$

Cancel the 4 in the numerator and denominator, then add 3 to each side of the equation.

$\left(x-1\right)^2=4\cdot\frac{\left(y-3\right)}{4}$

$f^{-1}\left(x\right)=\left(x-1\right)^2+3$

Are there any domain restrictions?