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  • If f(x) = x-1/x+1show that f(1/x) = -f(x)

If f(x)=\frac{x-1}{x+1}, then show that:

i)f(\frac{1}{x})=-f(x)   ii) f(-\frac{1}{x})=\frac{-1}{f(x)}

Answers (1)

Given data: f(x)=\frac{x-1}{x+1}

i) f(1/x) = \frac{\frac{1}{x}-1}{\frac{1}{x}+1}

= \frac{1-x}{1+x} 

= -(x-1)/x+1 = -f(x)

Thus, f(1/x) = -f(x)

ii)         f(-1/x) = \frac{\frac{-1}{x}-1}{\frac{-1}{x}+1}

= 1 + x/1 - x

=\frac{ 1}{1 + x/1 - x}

= -1/ f(x)

Thus, f(-1/x) = -1/f(x).

          

 

 

Posted by

infoexpert21

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