If (3, 6) lies on the boundary of the inequality y>f(x), the point that must be a solution to the inequality is

A. (0, 6)
B. (3, 3)
C. (3, 9)
D. (6, 6)

C maybe

f(3) = 6

so C is correct

To determine which point is a solution to the inequality y > f(x), we need to substitute each option's x and y values into the inequality and check if it holds true.

Given that (3, 6) lies on the boundary of the inequality, the point (3, 6) is a candidate for the solution. We will test it first:

Given y > f(x), substitute x = 3 and y = 6 into the inequality:
6 > f(3)

Since (3, 6) lies on the boundary, we can infer that it does not satisfy the strict inequality, and therefore is not a solution to y > f(x).

Now let's test the other options:

A. (0, 6):
6 > f(0) - We don't know the value of f(0), so we can't determine if this inequality is true.

B. (3, 3):
3 > f(3) - Same as before, we don't have enough information to know if this inequality is true.

C. (3, 9):
9 > f(3) - Since (3, 6) lies on the boundary, we need to find a point with a higher y-value. This point satisfies the inequality. Therefore, (3, 9) is a solution to y > f(x).

D. (6, 6):
6 > f(6) - Similar to the previous options, we don't have enough information to evaluate this inequality.

Based on our analysis, the point that must be a solution to the inequality y > f(x) is C. (3, 9).