If f(x)= x-1 x+1 , then show that. f (1 x )=-f(x) - Vidyadip

Question

If $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1},$ then show that.
$\text{f}\Big(\frac{1}{\text{x}}\Big)=-\text{f(x)}$

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Answer

Given that: $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1}$
$\text{f}\Big(\frac{1}{\text{x}}\Big)=\frac{\frac{1}{\text{x}}-1}{\frac{1}{\text{x}}+1}=\frac{1-\text{x}}{1+\text{x}}=\frac{-(\text{x}-1)}{\text{x}+1}=-\text{f(x)}$
Hence, $\text{f}\Big(\frac{1}{\text{x}}\Big)=-\text{f(x)}$

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