Question

If $f\left(x\right)=\left|x-2\right|$, where $x$ is a real number, then, which one of the following is correct?

• A. $f$ is periodic
• B. $f\left(x+y\right)=f\left(x\right)+f\left(y\right)$
• C. $f$ is an odd function
• D. $f$ is not one-one function
• E. $f$ is an even function

Answer 1

The correct option is D

$f$ is not one-one function

Explanation for the correct option:

Find the classification of function $f$:

Using the horizontal line test, if we draw a horizontal line to the graph of $f\left(x\right)=\left|x-2\right|$, it can be noticed that it intersects the graph at more than one point.

So for one value of $y$ in the range there are more than one value in the domain. Thus the function is not one-one.

Thus the function $f\left(x\right)=\left|x-2\right|$ is not one-one function.

Hence, the correct option is D.