What is the inverse of y= log_(1/2) (x+4) ?

1 Answer
Mar 4, 2018

The inverse is y=(1/2)^x-4

Explanation:

To find the inverse, switch x with y and vice versa, then solve for y. To convert out of log form, make it exponential form.

color(white)=>y=log_(1/2)(x+4)

=>color(red)x=log_color(blue)(1/2)color(green)((y+4))

color(white)=>color(green)(y+4)=color(blue)((1/2))^color(red)x

color(white)=>y=(1/2)^x-4

Here's a diagram of the graphs (I included the line y=x to show the reflection):

![https://www.desmos.com/calculator](useruploads.socratic.org)