Question

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

Answer 1

Answer:

Option (2) The graph of the inverse of h(x) is a vertical line

Step-by-step explanation:

A given expression in x i.e. y = f(x) will be a function if and only if there exists only one value of y for every value of x. In other words for any x belonging to its domain, there should not be more than one range. This can be checked easily if the grah of f(x) is known.

If we plot f(x) and draw a straight line parallel to y-axis from a point x belonging to its domain and this line meets the curve at only one point then f(x) will be a function. This test is called vertical line test.

So if the graph of inverse of h(x) passes the vertical line test then the inverse of h(x) is also a function.

Hope this helps.

Answer 2

Answer:

The second option.