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

f(g(x)) = x because g is the inverse of f, so its graph is the line y = x. That is the second option: the line through (-3,-3), (0,0), (3,3).