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Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$ (iv)\quad k(x)\;=\;x^2$

Note: This is the 4th part of a  4 part question, which is split as 4 separate questions here.

1 Answer

  • 1.A function f on set A is one-one if $f(x)=f(y) =>x,y \in A$
  • 2.A function f on set A is onto if for every $ y \in A$ then exists $x \in A$ such that $f(x)=y$
  • 3.A function is bijective if it is both one-one and onto
$ k(x)=x^2 \qquad [-1,1]$
Let $k(x_1)=x(x_2)=1 \qquad x_1x_2 \in [-1,1]$
$ k(-1)=(-1)^2=1$
Therefore $k(x_1)=k(x_2)$
does not imply $x_1=x_2$
Hence k is not one one
Let $y=-1$ then there is no element $x \in [-1,1]$ such that $k(x)=x^2=-1$
Hence k is not onto.
Hence k is neither one-one nor onto



answered Mar 4, 2013 by meena.p

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