The inverse of f(x)= x2 is also a function

The inverse is not a function because this function is not one-to-one, that is, a function [tex]f[/tex] has an inverse function if and only if there is no any horizontal line that intersects the graph of [tex]f[/tex] at more than one point, this is called the Horizontal Line Test for Inverse Functions. Thus, if you take an horizontal line it will pass through two points as indicated in the figure below. In conclusion, this function hasn't an inverse function.

mixter17 mixter17 · Answer 2 · 2019-03-07T02:39:44+01:00

Hello!

The answer is: False, the inverse of [tex]f(x)=x^{2}[/tex] is not a function.

Why?

It's known that most of functions don't have an inverse function. Inverse function is known for being the result of inverting a one to one function, it means that for each y should be only one x. If the function is not a one to one function, it doesn't have an inverse that is a function

The given function is not a one to one function, let's prove it:

Let's evaluate two differentes values: 5 and -5

Evaluating 5

[tex]f(5)=5^{2}=25[/tex]

Evaluating -5

[tex]f(-5)=(-5)^{2}=25[/tex]

We have the same output for differents x values, so, the function is not a one to one function, meaning that its inverse is not a function.

Have a nice day!