Answer:
[tex]x^2-10x+31[/tex]
Step-by-step explanation:
[tex]y=\sqrt{x-6}+5[/tex]
[tex]x=\sqrt{y-6}+5[/tex]
[tex]\sqrt{y-6}+5=x[/tex]
[tex]\sqrt{y-6}+5-5=x-5[/tex]
[tex]\sqrt{y-6}=x-5[/tex]
[tex]\left(\sqrt{y-6}\right)^2=\left(x-5\right)^2[/tex]
[tex]\left(\sqrt{y-6}\right)^2[/tex]
[tex]=\left(\left(y-6\right)^{\frac{1}{2}}\right)^2[/tex]
[tex]=y-6[/tex]
[tex]\left(x-5\right)^2[/tex]
[tex]=x^2-10x+25[/tex]
[tex]y-6=x^2-10x+25[/tex]
[tex]y-6+6=x^2-10x+25+6[/tex]
[tex]y=x^2-10x+31[/tex]
