Answer to Question #237900 in Calculus for CCW

Question

Unit 1 Review:

1) Find inverse of g(x) = 3x+1/ 2

Answer 1

$$g(x)=3x+\dfrac{1}{2}$$

Replace $g(x)$ and $y$

$$y=3x+\dfrac{1}{2}$$

Change $x$ and $y$

$$x=3y+\dfrac{1}{2}$$

Solve for $y$

$$y=\dfrac{1}{3}x-\dfrac{1}{6}$$

Replace $y$ and $g^{-1}(x)$

$$g^{-1}(x)=\dfrac{1}{3}x-\dfrac{1}{6}$$