Question

The point (7,−1) lies on the graph of g(x) . Which point must lie on the graph of g−1(x). A.) (7,-1) B.) (1,-7) C.) (-1,7) D.) (-7,-1)

Answer 1

To find a point on the inverse function g−1(x), you reverse the coordinates of the point on the original function g(x). Therefore, if (7,−1) is on g(x), then (−1,7) is on g−1(x).

Step-by-step explanation:

The question asks which point must lie on the graph of g−1(x), the inverse function of g(x), given the point (7,−1) lies on the graph of g(x). The coordinates of a point on the graph of an inverse function are the reverse of the corresponding point on the original function. Therefore, if the point (7,−1) lies on the graph of g(x), then the point (−1,7) must lie on the graph of g−1(x).

Answer 2

The correct answer is C) (−1, 7).

To find which point lies on the graph of g-1(x), [the inverse function of g(x)], given that the point (7, −1) lies on the graph of g(x), we need to understand the relationship between a function and its inverse.

For a function g(x) and its inverse g-1(x); if a point (a, b) lies on the graph of g(x), then the point (b, a) must lie on the graph of g-1(x). This is because, for the function g(x), a is the input and b is the output, similarly, for the inverse function g-1(x), b must be the input and a must be the output.

Given the point (7, −1) lies on g(x), to find the corresponding point on g-1(x), we swap the x and y coordinates. Thus, the x-co-ordinate becomes −1 and the y-co-ordinate becomes 7.

The point that lies on the graph of g-1(x) is (−1, 7).