if x belongs to R and a is any positive real number prove that modulus a is lesser than a is equal to minus a is less than x is less than a
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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.
Step-by-step explanation:
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