With inverse functions you just swap 'x' and 'y' and solve for 'y'.
[tex]\sf y=x^2-7[/tex]
Swap 'x' and 'y':
[tex]\sf x=y^2-7[/tex]
Add 7 to both sides:
[tex]\sf x+7=y^2[/tex]
Take the square root of both sides:
[tex]\sf y=\boxed{\sf\pm\sqrt{x+7}}[/tex]
