Answer:
[tex]y=\pm\sqrt{x+25}+5[/tex]
Step-by-step explanation:
Given function:
[tex]y=x^2-10x[/tex]
Rearrange to make [tex]x[/tex] the subject.
First, complete the square by adding 25 to both sides and factoring:
[tex]y+25=x^2-10x+25[/tex]
[tex]y+25=(x-5)^2[/tex]
Square root both sides:
[tex]\pm\sqrt{y+25}=x-5[/tex]
Add 5 to both sides:
[tex]x=\pm\sqrt{y+25}+5[/tex]
Finally, swap [tex]x[/tex] and [tex]y[/tex] (since the inverse of a function is its reflection in the line [tex]y = x[/tex])
[tex]y=\pm\sqrt{x+25}+5[/tex]
