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(x) = x + 1. The inverse function h(x) can be found by solving the equation y = x + 1 for x, which leads to h(x) = x - 1. Therefore, h(2) = 2 - 1 = 1.

A (-2) YOUR ANSWER

This choice suggests that h(2) equals -2, which would imply that g(-2) = 2. However, substituting -2 into the function g gives g(-2) = -2 + 1 = -1, not 2. Therefore, -2 cannot be the correct value for h(2).

B (0) YOUR ANSWER

Choosing 0 for h(2) means that g(0) should equal 2. By substituting into g, we find g(0) = 0 + 1 = 1, which is not equal to 2. Thus, this choice is incorrect.

C (1) CORRECT

This is the correct answer because if h(2) = 1, then g(1) should equal 2. Indeed, g(1) = 1 + 1 = 2, confirming that h(2) is indeed 1.

D (2) YOUR ANSWER

If h(2) = 2, that would mean g(2) = 2, which leads to g(2) = 2 + 1 = 3. This does not satisfy the condition h(2) = 2 and is therefore incorrect.

E (3) YOUR ANSWER

Choosing 3 implies that g(3) should equal 2. However, g(3) = 3 + 1 = 4, which does not equal 2. Therefore, this choice is also incorrect.

Conclusion

The inverse function h(x) of g(x) = x + 1 is derived by rearranging the equation to find that h(x) = x - 1. Plugging in 2 yields h(2) = 1, which is confirmed by the original function. Thus, understanding how to derive and evaluate inverse functions is crucial in solving such problems correctly.

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.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test