Question

Urgent I need the step by step on how to get this, I really appreciate it

Answer 1

Answer:

The inverse of f(x) is g(y)=$\frac{(y-8)^{2}}{4}+4$

Step-by-step explanation:

Given function is given by f(x)=$2\sqrt{x-4} +8$

Let, y=f(x)=$2\sqrt{x-4} +8$

and g(y)=x is inverse of f(x)

Now,

f(x)=$2\sqrt{x-4}+8$

y=$2\sqrt{x-4}+8$

y-8=$2\sqrt{x-4}$

$\frac{y-8}{2}=\sqrt{x-4}$

$\frac{(y-8)^{2}}{4}=(x-4)$

$\frac{(y-8)^{2}}{4}+4=x$

$\frac{(y-8)^{2}}{4}+4=x$

g(y)=x=$\frac{(y-8)^{2}}{4}+4$

Thus, the inverse of f(x) is g(y)=$\frac{(y-8)^{2}}{4}+4$