find the inverse function of...?

Question

f(x) = x^2 (0 smaller or equal to x smaller than positive infinity)

Answer 1

My teacher thought me this technique in inverse of a function

First, Change f(x) to y
f(x)= x^2
y=x^2

then reverse/transpose (i don't know the right term) x with y
y=x^2
x=y^2

then solve for y in terms of x
x=y^2
square root of x= square root of y^2
square root of x = y

finalize your answer by making y as f(x)^-1
f(x)^-1 = square root of x

*****
another example
find the inverse of a function of f(x)=2x+3
f(x)=2x+3
y=2x+3
x=2y+3
x-3=2y
(x-3) / 2 = y
f(x)^-1 = (x-3) / 2

therefore the inverse of a function of f(x) = 2x+3 is
f(x)^-1 (x-3) / 2

Answer 2

We seek a function g(x) such that f(g(x)) = x = g(f(x)). For
f(g(x)) we have (g(x))^2 = x, so g(x) = sqrt(x). (Notice that we can take the square root of x since 0 <= x.)

Check: g(f(x)) = sqrt(f(x)) = sqrt(x^2) = x.

The domain for g is 0 <= x < inf which is the range of f, and the range of g is 0 <= x < inf which is the domain for f.