Question 30

The value of h(0) is 2.

To find the value of h(0), we first need to evaluate the functions f and g at x = 0. Given that f(x) = e^x, we calculate f(0) = e^0 = 1. Since g(0) = 2, the product h(0) = f(0) * g(0) = 1 * 2 = 2.

A) 2

This option is correct because it reflects the calculation of h(0). With f(0) equal to 1 and g(0) equal to 2, the product h(0) = 1 * 2 gives us the value of 2.

B) e

This option is incorrect because it suggests that h(0) equals e. While f(0) = 1, which is part of the calculation, g(0) must also be included to determine h(0). Thus, simply stating e ignores the contribution of g(0).

C) e^2

This option is incorrect as it misrepresents the relationship between the functions. h(0) is derived from multiplying f(0) and g(0), which does not result in e^2. Instead, the correct evaluation leads to a value of 2.

D) e + 2

This option is also incorrect. It suggests adding e to 2, which does not correspond to the product of f(0) and g(0). The calculation for h(0) requires multiplication, not addition.

E) 2e

This option is incorrect because it implies that h(0) results in 2 multiplied by e. However, our calculation shows that the correct value derives from the multiplication of f(0) and g(0), leading to the value of 2, not 2e.

Conclusion

The correct answer is definitively 2, as it accurately reflects the calculation of h(0) based on the provided functions. All other options fail to represent the product of f(0) and g(0) correctly, either by miscalculating the values or by using incorrect mathematical operations.