Question

Given the point A(6,3) lies on the graph of g(x), and the point B(6,5) lies on the graph of h(x), where h(x)=(f∘g)(x), the corresponding point that lies on the graph of f(x) must be ?

A) (5,6)
B) (6,3)
C) (3,6)
D) (6,5)

Answer 1

The corresponding point that lies on the graph of f(x) is (6,3).

Step-by-step explanation:

To find the corresponding point that lies on the graph of f(x), we can use the fact that h(x)=(f∘g)(x), where g(x) contains the point A(6,3) and h(x) contains the point B(6,5). Since (f∘g)(x) represents the composition of functions f and g, we can conclude that g(6) = 3 and h(6) = 5.

Now, to find the corresponding point on the graph of f(x), we need to determine the value of x that satisfies g(6) = 3. Since g(x) contains the point A(6,3), we know that g(6) = 3.

Therefore, the corresponding point that lies on the graph of f(x) is (6,3). The answer is (B) (6,3).