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Which of the following pairs of functions are equal ?

(A) $f(x)=\large\frac{x}{|x|}$ $and\:\:g(x)=1$ (B) $f(x)=\sqrt {x^2}\:\:and\:\:g(x)=|x|$ (C) $f(x)=\large\frac{|x|}{x^2}$ $and\:\:g(x)=\frac{1}{x}$ (D) $f(x)=\sqrt {x^2}\:\:and\:\:g(x)=x$

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  • $|x|=x,$ if $x\geq 0$ and $|x|=-x$ if $x<0$
$\sqrt{x^2}=\pm x=|x|$
answered May 30, 2013 by rvidyagovindarajan_1
 

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