Question

Question #59f7b

Answer 1

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.