Questions in fun-lim

Select	Question
	If $f(x)=\cos (\log x)$, then $f(x)f(y)-\frac{1}{2}[f(x/y)+f(xy)]=$
	If $f(x)=\frac{1-x}{1+x},$ then $f[f(\cos \ 2\theta )]=$
	If $f(x)=\sin \log x$, then the value of $f(xy)+f\left( \frac{x}{y} \right)-2f(x).\cos \log y$ is equal to
	The value of b and c for which the identity $f(x+1)-f(x)=8x+3$ is satisfied, where $f(x)=b{{x}^{2}}+cx+d$, are
	Given the function $f(x)=\frac{{{a}^{x}}+{{a}^{-x}}}{2},\ (a>2)$. Then $f(x+y)+f(x-y)=$
	If $f(x)=\frac{x}{x-1}$, then $\frac{f(a)}{f(a+1)}=$
	If $f(x)=\cos (\log x)$, then $f({{x}^{2}})f({{y}^{2}})-\frac{1}{2}\left[ f\,\left( \frac{{{x}^{2}}}{2} \right)+f\left( \frac{{{x}^{2}}}{{{y}^{2}}} \right) \right]$ has the value
	The equivalent function of $\log {{x}^{2}}$ is
	If $f(x)=\log \left[ \frac{1+x}{1-x} \right]$, then $f\left[ \frac{2x}{1+{{x}^{2}}} \right]$ is equal to
	If $\varphi (x)={{a}^{x}}$, then ${{\{\varphi (p)\}}^{3}}$is equal to

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