Q. 65.0( 1 Vote )

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Answer :

To prove: function is one-one and into


Given: f : Z Z : f (x) = x3


Solution: We have,


f(x) = x3


For, f(x1) = f(x2)


x13 = x23


x1 = x2


When, f(x1) = f(x2) then x1 = x2


f(x) is one-one


f(x) = x3


Let f(x) = y such that


y = x3



If y = 2, as


Then we will get an irrational value of x, but


Hence f(x) is into


Hence Proved


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