Question

Devy likes to learn! Could someone please tell me how to answer this question?

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).

On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).

On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).

On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).

Answer 1

B

Explanation:

Recall that if two functions, f and g, are inverses, then by definition:

`\displaystyle f(g(x)) = g(f(x)) = x`

Hence, the graph of f(g(x)) should be simply y = x.

Therefore, our answer is B, as both coordinates are equivalent for all three points.