Question 43

h(2) equals 1.

To find the value of h(2), we need to determine the inverse function of g(x) = x + 1. The inverse function h(x) can be found by solving the equation y = x + 1 for x, which yields h(x) = x - 1. Thus, h(2) = 2 - 1 = 1.

A) -2

This option is incorrect because substituting -2 into the inverse function would yield h(-2) = -2 - 1 = -3, which does not relate to the value of h(2).

B) 1

This option is correct as h(2) = 2 - 1 = 1, accurately reflecting the definition of the inverse function of g.

C) 1

This option is the correct answer. As shown, when we calculate h(2) using the inverse function h(x) = x - 1, we find that h(2) equals 1.

D) 2

This option is incorrect because if h(2) were 2, it would imply that 2 + 1 = 2, which contradicts the definition of the function g(x).

E) 3

This option is also incorrect. If h(2) were 3, it would imply that 3 + 1 = 2, which is not true according to the inverse function of g.

Conclusion

The correct answer is C, as h(2) = 1 is derived directly from the calculation of the inverse function of g(x). All other options fail because they do not satisfy the conditions set by the function g and its inverse h.