Question

Which of the following is the domain and range of the inverse of y = 2√x - 6+4?

A. The domain is x2 4; the range is y≥ 6.
B. The domain is x≥ 6; the range is y≥ 4.
C. The domain is x2 4; the range is y≥ 8.
D. The domain is x2 12; the range is y≥ 4.

Answer 1

The domain of the inverse is y ≥ 1 and the range of the inverse is x ≥ 0.

Step-by-step explanation:

The given equation is y = 2√x - 6+4. To find the domain and range of the inverse, we need to interchange the x and y variables. So, the inverse equation is x = 2√y - 6+4. To find the domain of the inverse, we need to consider the restrictions on the variables. Since the square root can only take non-negative values, the expression inside the square root (2√y - 6+4) must be greater than or equal to 0. Solving for y, we have 2√y - 6+4 ≥ 0. Simplifying, we get √y ≥ 1, which gives us y ≥ 1. Therefore, the domain of the inverse is y ≥ 1. To find the range of the inverse, we need to consider the values of x. Since the original equation had a square root, we need to find the range of the original equation, which is y = 2√x - 6+4. Since the square root can only take non-negative values, x must be greater than or equal to 0. Therefore, the range of the inverse is x ≥ 0.

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