Answer:
The inverse of f(x) is g(y)=[tex]\frac{(y-8)^{2}}{4}+4[/tex]
Step-by-step explanation:
Given function is given by f(x)=[tex]2\sqrt{x-4} +8[/tex]
Let, y=f(x)=[tex]2\sqrt{x-4} +8[/tex]
and g(y)=x is inverse of f(x)
Now,
f(x)=[tex]2\sqrt{x-4}+8[/tex]
y=[tex]2\sqrt{x-4}+8[/tex]
y-8=[tex]2\sqrt{x-4}[/tex]
[tex]\frac{y-8}{2}=\sqrt{x-4}[/tex]
[tex]\frac{(y-8)^{2}}{4}=(x-4)[/tex]
[tex]\frac{(y-8)^{2}}{4}+4=x[/tex]
[tex]\frac{(y-8)^{2}}{4}+4=x[/tex]
g(y)=x=[tex]\frac{(y-8)^{2}}{4}+4[/tex]
Thus, the inverse of f(x) is g(y)=[tex]\frac{(y-8)^{2}}{4}+4[/tex]
