If F (x) and G (x) are inverse functions, which statement must be true? A. F (G (x)) = 1 B. F (G (x)) = x C. F (x) = 1/G (X) D. F (X) = - G (X)

The correct answer is:

B) f (g (x)) = x.

Explanation:

A composition of two inverse functions undoes everything except the variable used.

Using x, g (x) will perform some action to x. f (x), since it is the inverse of g (x), will undo the action that g (x) performed; this will simply leave x.

For example, let f (x) = x-3. To find the the inverse, g (x), we will first replace f (x) = with y=:

y = x-3

Now we switch x and y:

x = y-3

To isolate y, we add 3 to each side:

x+3 = y-3+3

x+3 = y

Now we write this as g (x):

g (x) = x+3

We now perform the composition f (g (x)):

g (x) = x+3

f (g (x)) = f (x+3) = x+3-3 = x

It’s actually F (G (x)) = x. I plugged in the other answer and got it wrong.