Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1 question 3
, given byis one-one but not onto.
Let x and y be any two elements in the domain (N), such that
So,f is one-one.
, defined by
Let us prove that the given function is one-one.
We have … (i)
Calculate … (ii)
Now equate equation (i) and (ii)
From (iii) equation, we can write
, because if we substitute
Hence, for any
So,f is a one-one function.
But, for all
So, doesn’t assume values of1 and 2
is not an onto function.
Hence, we proved that, is one-one function not an onto function.
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