if f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?
if f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?
Answer
Explanation:
Step1: Recall inverse - function property
If (f(x)) and (g(x)) are inverse functions of each other, then for all (x) in the domain of (g), (f(g(x))=x).
Step2: Identify the graph of (y = x)
The equation (y = x) is a straight - line with a slope of (1) and a (y) - intercept of (0). It passes through the origin ((0,0)) and has points such as ((1,1)), ((- 1,-1)) etc.
Answer:
The graph that is a straight - line passing through the origin with a slope of (1) (the first graph shown in the image where the line goes through points like ((-1,-1)), ((0,0)), ((1,1)) etc.) represents the graph of (f(g(x))).