which statement could be used to explain why the function h(x) = x³ has an inverse relation that is also a…

which statement could be used to explain why the function h(x) = x³ has an inverse relation that is also a function?\nthe graph of h(x) passes the vertical line test.\nthe graph of the inverse of h(x) is a vertical line.\nthe graph of the inverse of h(x) passes the horizontal line test.\nthe graph of h(x) passes the horizontal line test.

which statement could be used to explain why the function h(x) = x³ has an inverse relation that is also a function?\nthe graph of h(x) passes the vertical line test.\nthe graph of the inverse of h(x) is a vertical line.\nthe graph of the inverse of h(x) passes the horizontal line test.\nthe graph of h(x) passes the horizontal line test.

Answer

Answer:

D. The graph of (h(x)) passes the horizontal line test.

Explanation:

Step1: Recall function - inverse function concept

A function (y = f(x)) has an inverse that is also a function if and only if (f(x)) is one - to - one.

Step2: Understand line tests

The vertical line test is used to determine if a relation is a function. A horizontal line test is used to determine if a function is one - to - one.

Step3: Analyze the function (h(x)=x^{3})

For the function (h(x)=x^{3}), if we want its inverse to be a function, (h(x)) must be one - to - one. The graph of (h(x)=x^{3}) passes the horizontal line test, which means for every (y) value there is exactly one (x) value. So its inverse relation is also a function.