# Show that the Modulus Function f : R → R, given by f (x) = |x|, is neither one-one nor onto, where |x| is x, if x is positive or 0 and |x| is – x, if x is negative.

It is given that f : R → R, given by f (x) = | x|

We can see that f(-1) = |-1| = 1, f(1) = |1| = 1

⇒ f(-1) = f(1), but -1 ≠ 1.

⇒ f is not one-one.

Now, we consider -1 ϵ R.

We know that f(x) = |x| is always positive

Therefore, there doesn't exist any element x in domain R such that f(x) = |x| = -1

⇒ f is not onto.

Therefore, modulus function is neither one-one nor onto.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 0152 mins
Different kind of mappings58 mins
Functions - 0648 mins
Functions - 1156 mins
Some standard real functions61 mins
Quick Revision of Types of Relations59 mins
Range of Functions58 mins
Battle of Graphs | various functions & their Graphs48 mins
Functions - 0947 mins
Quick Recap lecture of important graphs & functions58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses