What is the inverse of f (x) = (x-5) ^2 for x≥5 where function g is the inverse of function f?

Let f (x) = y

y = (x-5) ^2

x-5 = sqrt y

x = sqrt y + 5

f-1 (x) = sqrtx + 5

g (x) = sqrt x + 5 for x > = 5

Say, for example, that a function f acts on 5, producing f (5). Then if g is the inverse of f, then g acting on f (5) will bring back 5.

g (f (5)) = 5.

Actually, g must do that for all values in the domain of f. And f must do that for all values in the domain of g.

In general, if a function f acts on a value of x, producing f (x),

then if g is the inverse, then g acting on f (x) - - g (f (x)) - - will return x.

Here is the definition:

Functions f (x) and g (x) are inverses of one another if:

f (g (x)) = x and g (f (x)) = x,

for all values of x in their respective domains.