Q. 44.5( 2 Votes )

Show that the fun

Answer :

To prove: function is one-one and into


Given: f : N N : f (x) = x2


Solution: We have,


f(x) = x2


For, f(x1) = f(x2)


x12 = x22


x1 = x2


Here we can’t consider x1 = -x2 as , we can’t have negative values


f(x) is one-one


f(x) = x2


Let f(x) = y such that


y = x2



If y = 2, as


Then we will get the irrational value of x, but


Hence f(x) is not into


Hence Proved


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