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Show that the function \(f : R \to R\) given by \(f (x) = x^3\) is injective.
cbse
class12
bookproblem
ch1
misc
q5
p29
sec-a
easy
math
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asked
Nov 21, 2012
by
vaishali.a
retagged
Mar 20, 2013
by
balaji.thirumalai
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A function $f: X \rightarrow Y$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
Given $f : R \to R$ define by $f(x) = x^3$
A function $f: X \rightarrow Y$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
Let $f(x)=f(y) \rightarrow$ $x^3=y^3$
This is possible only if $x=y \rightarrow f$ is injective.
answered
Feb 27, 2013
by
meena.p
edited
Mar 20, 2013
by
balaji.thirumalai
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