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If $f(x)=\large\frac{4^x}{4^x+2}$ then which among the following is correct ?

$\begin{array}{1 1}f(x)=f(1-x) \\ f(x)+f(1-x)=0 \\ f(x)+f(1-x)=1 \\ f(x)+f(x-1)=1 \end{array}$

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1 Answer

$f(x)=\large\frac{4^x}{4^x+2}$
$f(1-x)=\large\frac{4^{1-x}}{4^{1-x}+2}$
$=\large\frac{4}{4+2\times 4^x}$ $=\large\frac{2}{2+4^x}$
$f(x)+f(1-x)=\large\frac{4^x+2}{4^x+2}$ $=1$
answered May 21, 2013 by rvidyagovindarajan_1
 
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