The function h is the product of the functions f and g, where f(x) = e^x and g(0) = 2. What is the value of h(0)?

Rationale

h(0) equals 2.

To find the value of h(0), we apply the definition of the function h as the product of f and g. Given that f(x) = e^x and g(0) = 2, we can compute h(0) as follows: h(0) = f(0) * g(0) = e^0 * 2 = 1 * 2 = 2.

A (2) CORRECT

This is the correct answer. We calculated h(0) by substituting x = 0 into the function definitions: f(0) = e^0 = 1 and g(0) = 2. Therefore, h(0) = 1 * 2 = 2.

B (e) YOUR ANSWER

This choice suggests that h(0) equals the mathematical constant e. However, h(0) is the product of f(0) and g(0). Since f(0) equals 1, h(0) cannot simply be e, as it also requires the multiplication by g(0), which is 2.

C (e^2) YOUR ANSWER

This option implies that h(0) is e squared. While f(0) equals 1, g(0) is 2, thus h(0) cannot equal e^2, which arises from incorrect multiplication of the function values.

D (e + 2) YOUR ANSWER

This choice indicates a sum of e and 2, which misinterprets the definition of h as a product rather than a sum. The correct calculation for h(0) is based on multiplication, not addition.

E (2e) YOUR ANSWER

This option suggests that h(0) equals 2 times e. While g(0) is indeed 2, f(0) contributes a value of 1. Therefore, h(0) is not equal to 2e, as this would imply an incorrect evaluation of f(0).

Conclusion

The function h(0) is determined by the product of f(0) and g(0). With f(0) calculated as 1 and g(0) as 2, we find h(0) = 1 * 2 = 2. All other options fail to reflect the correct application of the product rule, confirming that 2 is indeed the accurate value of h(0).

The function h is the product of the functions f and g, where f(x) = e^x and g(0) = 2. What is the value of h(0)?

h(0) equals 2.

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