Question

If f(x) = (x – 3)2 + 4 and g(x) = x2 + 2, which statement is true?

F (-2) = g(-3)
G f(0) = g(-1)
H F(8) = g(3)
J f(2) = g(1)

Answer 1

None of the statements F, G, H, or J is true as the calculated values of f(x) do not match with the corresponding g(x) values.

Step-by-step explanation:

To determine which statement is true, we need to evaluate the functions f(x) and g(x) at the specified values and compare the results. Let's do that for each option:

• For option F, we check if f(-2) equals g(-3). We calculate f(-2) = ((-2) - 3)^2 + 4 = (-5)^2 + 4 = 25 + 4 = 29, and g(-3) = (-3)^2 + 2 = 9 + 2 = 11. Since 29 is not equal to 11, option F is not correct.
• For option G, we check if f(0) equals g(-1). We calculate f(0) = ((0) - 3)^2 + 4 = (-3)^2 + 4 = 9 + 4 = 13, and g(-1) = (-1)^2 + 2 = 1 + 2 = 3. Since 13 is not equal to 3, option G is not correct.
• For option H, we check if f(8) equals g(3). We calculate f(8) = ((8) - 3)^2 + 4 = (5)^2 + 4 = 25 + 4 = 29, and g(3) = (3)^2 + 2 = 9 + 2 = 11. Since 29 is not equal to 11, option H is not correct.
• For option J, we check if f(2) equals g(1). We calculate f(2) = ((2) - 3)^2 + 4 = (-1)^2 + 4 = 1 + 4 = 5, and g(1) = (1)^2 + 2 = 1 + 2 = 3. Since 5 is not equal to 3, option J is not correct.

Upon evaluating all the options, it turns out that none of them are correct since the values of f(x) do not match the corresponding values of g(x) for the given x values