If fx-x-1x-1 the show that fx-f1x-0

f(x)=x+1x 1 f(1x)=1x+11x 1 =1+xx1 xx =1+x1 x=x+1 (x 1)= x+1x 1 f(x)+f(1x)=x+1x 1 x+1x 1=0 Hence proved. ...

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Composite Function

If fx=x+1x-...

Question

If $f (x) = \frac{x + 1}{x - 1}$ the show that $f (x) + f (\frac{1}{x}) = 0$

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If $f (x) = x^{3} - \frac{1}{x^{3}}$ , show that $f (x) + f (\frac{1}{x} = 0)$ .

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

f : R - {1} \to R

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

f (x) + f (\frac{1}{x}) = 0

(x \neq 0)

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

f (x) + f (\begin{matrix} 1 x \end{matrix}) = 0

f (x) = \frac{4^{x}}{4^{x} + 2} for all x \in R .

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