Answer: f⁻¹(x)=(x-7)²
Step-by-step explanation:
To find the inverse function, we want to switch the y with the x and vice versa. Then we solve for y.
[tex]y=\sqrt{x} +7[/tex] [switch y with x and x with y]
[tex]x=\sqrt{y} +7[/tex] [subtract both sides by 7]
[tex]x-7=\sqrt{y}[/tex] [square both sides]
[tex]y=(x-7)^2[/tex]
Now, we know that f⁻¹(x)=(x-7)².
