Question

Which equation is the inverse of y = 100 - x^2?

A. y = 2√(100 - 8)
B. y = 102√
C. y = 100^2√
D. y = √(x-100)

Answer 1

To find the inverse of the function y = 100 - x^2, we swap x and y and solve for y to obtain y = √(100 - x). None of the provided options match exactly, but option D appears to have a typo and should be y = √(100 - x), which would be the correct inverse.

Step-by-step explanation:

The question is asking to find the inverse of the function y = 100 - x2. To find the inverse of a function, you swap x and y and solve for y. Let's do this step by step:

1. First, we replace y with x in the original equation: x = 100 - y2.
2. Next, we solve this equation for y. To do this, we first add y2 to both sides: y2 = 100 - x.
3. Then we take the square root of both sides to get y by itself: y = ±√(100 - x). We only consider the positive square root since the original function is a downward-opening parabola, and we're interested in the inverse for y ≥ 0.

When we compare the options provided, we look for the one that matches our derived form of the inverse. None of the options match exactly, so we must identify a typographical error in the question. None of the options A, B, or C are correct inverse forms, but option D seems to be a typo and should read y = √(100 - x), which would then be the correct inverse.