Question

If f(x) = 4 – x² and g(x) = 6x, which expression is equivalent to (9 - 1)(3)?

a) 6 - 3 - (4 + 3)
b) 6 - 3 - (4 - 3²)
c) 6(3) – 4 + 3²
d) 6(3) – 4 - 3²

Answer 1

None of the given options matches the result of (9 - 1)(3), which simplifies to 24. However, if the question meant to ask for (g(3) - f(3)), the expression equivalent to this using the functions provided would be 6(3) – 4 + 3², and the correct answer would be 23, which is Option c). There seems to be a misunderstanding or error in the question as written.

Step-by-step explanation:

To find which expression is equivalent to (9 - 1)(3), first perform the calculation within the parentheses, which simplifies to 8(3) or 24. Now we need to match that result to the expressions given, accounting for the functions f(x) and g(x) provided:

• f(x) = 4 - x²
• g(x) = 6x

Looking at each option, we evaluate accordingly:

1. Option a) is 6 - 3 - (4 + 3) which equals -1, not 24.
2. Option b) is 6 - 3 - (4 - 3²) which equals 6 - 3 - (4 - 9) = 6 - 3 + 5 = 8, not 24.
3. Option c) is 6(3) – 4 + 3² which equals 18 - 4 + 9 = 23, not 24.
4. Option d) is 6(3) – 4 - 3² which equals 18 - 4 - 9, which simplifies to 18 - 13 = 5, not 24.

It appears there is an error, as none of the options provided match the result of (9 - 1)(3). However, based on the functions provided, it could be that the question is asking for the expression (g(3) - f(3)). Calculating that gives us:

• g(3) = 6(3) = 18
• f(3) = 4 - 3² = 4 - 9 = -5
• Therefore, g(3) - f(3) = 18 - (-5) = 18 + 5 = 23

This result matches Option c), suggesting that the original question may have intended to ask for the evaluation of (g(3) - f(3)) rather than (9 - 1)(3).