Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f of x equals four divided by x. and g of x equals four divided by x

Given f(x) = ⁴/ₓ and g(x) = ⁴/ₓ.

Based on the work steps above, it appears that thus it has been confirmed that f and g are inverses.

Part-A

Let

Rewrite and set the function with subject x.

Both sides are divided by x.

Both sides are divided by y.

Let's replace and .

Thus, the inverse of

Part-B

Let

Rewrite and set the function with subject x.

Both sides are divided by x.

Both sides are divided by y.

Let's replace and .

Thus, the inverse of

Notes:

Keywords: the inverse of function, confirm that f and g are inverses, by showing that f(g(x)) = x, g(f(x)) = x, four divided by x, one-to-one, onto

Here's what we know:

To find f(g(x)), we must plug g(x) for every x in f(x). This looks like:

Now we must check g(f(x)):

We end up getting the exact same thing.

Since , f and g are inverses.