TIP: – One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.
So, is One – One function
⇒ f(a)≠f(b) for all
⇔ f(a) = f(b)
⇒ a = b for all
Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.
So, is Surjection iff for each , there exists such that f(a) = b
Bijection Function: – A function is said to be a bijection function if it is one – one as well as onto function.
Now, f : R → R, defined by f(x) = |x|
Check for Injectivity:
Let x,y be elements belongs to R i.e such that
⇒ x = y
⇒ |x| = |y|
⇒ – x = y
⇒ | – x| = |y|
⇒ x = |y|
Hence from case i and case ii f is not One – One function
Check for Surjectivity:
Since f attain only positive values, for negative real numbers in R
(co – domain) there is no pre–image in domain R.
Hence, f is not onto function
Thus, Not Bijective also
Rate this question :