Answer: [tex]f^{-1}(x)=2x-6[/tex]
Step-by-step explanation:
To find the inverse, we want to switch the y with x and x with y. Once we do that, we solve for y.
[tex]y=\frac{1}{2}x+3[/tex] [switch x and y]
[tex]x=\frac{1}{2}y+3[/tex] [subtract both sides by 3]
[tex]x-3=\frac{1}{2} y[/tex] [multiply both sides by 2]
[tex]y=2x-6[/tex]
Now, we know that [tex]f^{-1}(x)=2x-6[/tex].
