+9 Given that (-2, 3) is on the graph of y = f(x), find a point that must be on the graph of y = f(2x+1)+3 . Express your answer as an ordered pair (a, b) where a and b are real numbers.
Since (-2, 3) is on the graph of y = f(x), we know that f(-2) = 3.
Let (a, b) be a point on the graph of y = f(2x+1)+3. This means that f(2a+1) + 3 = b.
Substituting f(-2) = 3 into the equation f(2a+1) + 3 = b, we get 3 + 3 = b .
Therefore, b = 6 and the point (a, b) = (a, 6) must be on the graph of y = f(2x+1)+3.
Note: We can also find the value of a by substituting b = 6 into the equation f(2a+1) + 3 = b. This gives us f(2a+1) = 3, so f(2a+1) = f(-2). Since (-2, 3) is on the graph of y = f(x), we know that f(-2) = 3, so f(2a+1) = 3. This means that 2a+1 = -2, so a = -3. Therefore, the point (a, b) = (-3, 6) must be on the graph of y = f(2x+1)+3.
