Question

Are the functions f(x) and g(x) inverse of one another?

Answer 1

No!

Step-by-step explanation:

The function
`f(x)` doesn't have inverse because it doesn't pass the horizontal line test. This test tells us that a function
`f` has an inverse function if and only if there is no any horizontal line that intersects the graph of
`f` at more than one point. As you can see, from the graph of f (the red one), if you draw an horizontal line that passes through
`y=4` then this line will touch the graph of f at three points, so the horizontal line test is not satisfied here. If you see the graph of g, this doesn't represent a function because there is at least one vertical line that touches the graph at more than one point, so this relation is not a function.