The function g is defined by g(x) = x + 1. If h is the inverse function of g, what is the value of h(2)?

Rationale

h(2) equals 1.

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

A (-2) YOUR ANSWER

If we substitute -2 into the inverse function, we would get h(-2) = -2 - 1 = -3. This value does not correspond to h(2) and is therefore incorrect.

B (0) YOUR ANSWER

Substituting 0 into the inverse function yields h(0) = 0 - 1 = -1. This result does not equal 1, making it an incorrect choice for h(2).

C (1) CORRECT

This is the correct choice. As derived from the inverse function h(y) = y - 1, substituting 2 gives us h(2) = 2 - 1 = 1. This value correctly represents h(2).

D (2) YOUR ANSWER

If we were to set h(2) = 2, this would imply that g(2) = 2 + 1 = 3, and thus h(3) = 2. This contradicts our earlier calculation of h(2) = 1, making this option incorrect.

E (3) YOUR ANSWER

Setting h(2) = 3 would imply that g(3) = 3 + 1 = 4, which does not correspond to our calculation of h(2). Therefore, this option is also incorrect.

Conclusion

The function h, being the inverse of g, can be calculated as h(y) = y - 1. By substituting 2 into this inverse function, we find that h(2) equals 1. All other options do not satisfy the condition set by the inverse function, confirming the correct answer is 1.

The function g is defined by g(x) = x + 1. If h is the inverse function of g, what is the value of h(2)?

h(2) equals 1.

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