Question 9

h(2) equals 1

To find h(2), we need to determine the inverse function of g(x) = x + 1. The inverse function h will reverse the operation of g, allowing us to solve for h(2) effectively.

A) -2

This option is incorrect because if h(2) were -2, it would imply that g(-2) equals 2. However, g(-2) equals -1, not 2, which does not satisfy the definition of the inverse function.

B) [Blank]

This option is not applicable as it is blank.

C) 1

This option is correct. To find h(2), we set g(x) = 2. Solving the equation x + 1 = 2 gives x = 1, which means h(2) = 1. This satisfies the condition that h is the inverse of g.

D) 2

This option is incorrect because if h(2) were 2, then g(2) would need to equal 2. However, g(2) equals 3, which does not satisfy the relationship required for the inverse function.

E) 3

This option is also incorrect. If h(2) were 3, then g(3) would have to equal 2. However, g(3) equals 4, not 2, which does not meet the criteria for the inverse function.

Conclusion

The correct answer is C) 1, as it accurately reflects the value of the inverse function h at the point where g(x) equals 2. All other options fail to satisfy the necessary conditions for inverse functions, demonstrating the importance of correctly identifying how functions and their inverses interact.