Leonard wants to restrict the domain of the tangent function so that its inverse is a function. which description best describes how he could restrict the domain? a) choose any interval between consecutive asymptotes. b) choose any interval that includes two asymptotes. c) choose any interval of length 2π radians. d) choose any interval of length π radians.

Correct choice is A

Step-by-step explanation:

If a function has an inverse, then there is at most one x-value for each y-value.

The tangent function is periodic with period Hence, at each value for which is defined, for each integer n. Therefore, the function does not have an inverse. Since tangent is not a one-to-one function, the domain must be limited. From examining the graph of the tangent function, we see that in each interval of the form

where k is an integer, the tangent function assumes every value in its range. Moreover, in each such interval, each y-value is achieved exactly once. Hence, we can create an invertible function by restricting the domain tangent function to one such interval. Such interval is an interval between two consecutive vertical asymptotes and