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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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True or False: Every function is invertible.

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  • A function f is invertible if it is one-one and onto
A function $f:N \to N$
 
$f(x)=x^2$
 
Let $x_1\; and\; x_2$ be such that $x_1,x_2 \in N$
 
$f(x_1)=f(x_2)$
 
$=>x_1=x_2$
 
But we see that for $y=2 \in N$
 
There does not exist $f(x)=2$
 
Therefore f is not onto
 
f is not invertible
 
Hence the given statement is 'False'

 

answered Mar 6, 2013 by meena.p
 

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