Question

6. Consider the modulus function f(x) = xl.
(a) Find the domain and range of the function f(x) = \xl.
6) Draw the graph of the function f(x) = [xl.​

Answer 1

Answer:

f(x)=∣x∣={

x if x>0

−x if x<0

It is seen that f(−1)=∣−1∣=1,f(1)=∣1∣=1∴f(−1)=f(1), but −1

=1

∴f is not one-one

Now, consider −1∈R.

but it is known that f(x)=∣x∣ is always non-negative.

Thus, there does not exist any element x in domain R such that f(x)=∣x∣=−1

∴f is not onto.

Hence, the modulus function is neither one-one nor onto.