Page No 11:
Question 4:
Show that the Modulus Function f: R → R given by
, is neither one-one nor onto, where
is x, if x is positive or 0 andis − x, if x is negative.
f: R → R is given by,
It is seen that
.
∴f(−1) = f(1), but −1 ≠ 1.
∴ f is not one-one.
Now, consider −1 ∈ R.
It is known that f(x) = is always non-negative. Thus, there does not exist any element x in domain R such that f(x) = = −1.
∴ f is not onto.
Hence, the modulus function is neither one-one nor onto.
