Question #59f7b

1 Answer
Jan 2, 2018

Answer:

See the explanation.

Explanation:

If a function #f(x)# has an inverse, it must be bijective, or one-to-one onto.

http://physicscatalyst.com/maths/relation_and_function_12_1.php

The figure is the example of a bijective function. If you choose one element from the right elipse, you can know the corresponding element in the left oval.

It is a good way to draw a graph of the function if you want to know whether it is bijective.

#f(x)=2x+1# is bijective.
graph{2x+1 [-5, 5, -5, 5]}

#f(x)=x^2# is not bijective.
graph{x^2 [-5, 5, -5, 5]}

Then, how about #f(x)=xtan((pix)/2)#?
graph{xtan((pix)/2) [-1, 1, -5, 5]}

The function #f(x)=xtan((pix)/2)# #(-1< x< 1)# is not bijective.
For example, #f(1/2)=f(-1/2)=1/2#.
Therefore, it has no inverse.