Question

Which statement could be used to explain why f(x)=2x-3 has an inverse relation that is a function

Answer 1

The correct answer is:

The function is a one-to-one function.

Explanation:

When an equation is graphed, we use the Vertical Line Test to determine if that equation is a function; if a vertical line hits more than one point anywhere on the graph, the graph is not a function.

This corresponds with the definition of a function:  A function is a set of ordered pairs in which each element of the domain (x) is mapped to no more than one element of the range (y).  Since every x has no more than one y, there will be no two points hit by the same vertical line.

When we have the graph of a function, to determine if it has an inverse, we use the Horizontal Line Test: if a horizontal line hits more than one point anywhere on the graph, the function does not have an inverse.

This corresponds with the definition of a one-to-one function:  A function in which every element of the range (y) is mapped to exactly one element of the domain (x). Since every y has one x, there will be no horizontal line that hits more than one point anywhere on the graph.

Answer 2

An inverse function is the relation formed when the independent variable is exchanged with the dependent variable in a given relation. To find this you just have to swap the x and y coordinates. The statement that could be used in this problem to explain why f(x) = 2x - 3 has an inverse relation that is a function is: B) f(x) is a one to one function.

I hope it helps, Regards.