verify that function f(x) is the inverse of function g(x)?

Question

f(x) = x² + 4 , x is greater than or equal to 0

g(x) = square root of x - 4 , x is greater than or equal to 4

Answer 1

f(g(x)) = x-4+4 = x
g(f(x)) = sqrt(x^2+4-4) = x
Hence they are inverse of each other

Answer 2

There is a two-step process to check if one function is the inverse of another (or to find the inverse of a given function:

1. switch variables in one function, that is, switch x and y

2. solve for y

For your function f(x) = y = x^2 +4 switch x and y to get

x = y^2+4

Now solve for y in the new equation

y^2 = x-4 so

y = sqrt(x-4) as long as x is > or = to 4 so that the

sqrt is defined. You can call this new function

f^-1(x) or g(x) = sqrt(x-4)

If you calculate f[g(x)] you should get x since they are inverses.
f[g(x)] = [sqrt(x-4)]^2+4 = x-4 + 4 = x

Therefore g(x) and f(x) are inverses.

Answer 3

Plug one equations into the other for x. I plugged g(x) into f(x) for x.

0 = (square root of x-4)squared + 4

the square root and squared will cancel each other out leaving you with...

0 = x - 4 + 4 subtract 4 from both sides
-4 = x - 4 add 4 to both sides
0 = x x = 0 and the limit is x can be greater than or equal to 0 and it is.