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question_answer1) If \[f:R\to R,\,\,f\left( x \right)=2{{x}^{3}}-7,\]then find pre image of 9 under f.
question_answer2) Find the period of the function satisfying the relation\[f\left( x \right)+f\left( x+3 \right)=0\,\,\forall \,\,x\in \,\,R\].
question_answer3) If \[f\left( x \right)\] is a function satisfying \[f\left( x+y \right)=f\left( x \right)\,\,f\left( y \right)\] for all \[x,\,\,y\,\,\in \,\,N\] such that \[f\left( 1 \right)=3\] and \[\sum\limits_{x=1}^{n}{f\left( x \right)}=120,\] then find the value of n.
question_answer4) Find the number of integers lying in the domain of the function \[f\left( x \right)=\sqrt{{{\log }_{\left( 0.5 \right)}}\left( \frac{5-2x}{x} \right)}.\]
question_answer5) If the range of the function \[f\left( x \right)={{6}^{x}}+{{3}^{x}}+{{6}^{-x}}+{{3}^{-x}}+2\]is \[[k,\infty )\]then find k.
question_answer6) Find period of function \[{{2}^{\left\{ x \right\}}}+\sin \,\,\pi x+{{3}^{\left\{ x/2 \right\}}}+\cos \,\,2\pi x\] is \[\left( where\{\,\}represent\,\,fractional\,\,part\,\,of\,\,x \right)\]
question_answer7) If period of \[\frac{\cos \left( \sin \,\,nx \right)}{\tan \left( x/n \right)}\left( n\in \,\,N \right)\] is \[6\pi \] then find value of n.
question_answer8) If \[f:R\to R\] satisfies \[f\left( x+y \right)=f\left( x \right)+f\left( y \right),\] for all \[x,\,\,y\,\,\in \,\,R\] and \[f\left( 1 \right)=7,\]\[\sum\limits_{r=1}^{n}{f\left( r \right)}=k\left( n \right)\left( n+1 \right)\] then find k.
question_answer9) Let \[f\left( x \right)=\frac{{{9}^{x}}}{{{9}^{x}}+3}\] and \[f\left( x \right)+f\left( 1-x \right)=1\] then find value of \[f\left( \frac{1}{1996} \right)+\left( \frac{2}{1996} \right)+....+f\left( \frac{1995}{1996} \right).\]
question_answer10) If
question_answer11) If f is a function such that \[2\,\,f\left( x \right)+f\left( 2-x \right)={{x}^{2}}\] then find value of \[f\left( 4 \right)\].
question_answer12) If \[f\left( x \right)\] is a polynomial function such that \[f\left( x \right).\,f\left( 1/x \right)=f\left( x \right)+f\left( 1/x \right)\]and \[f\left( 2 \right)=9\] then find value of \[f\left( 4. \right)\]
question_answer13) If the period of \[f\left( x \right)=\frac{1}{2}\left( \frac{\left| \sin \,\,x \right|}{\cos \,\,x}+\frac{\left| \cos \,\,x \right|}{\sin \,\,x} \right)\] is \[k\pi \] then find k.
question_answer14) If \[f\left( x \right)=\cos \left( \log \,\,x \right),\]then find value of\[\frac{f\left( xy \right)+f\left( x/y \right)}{f\left( x \right)f\left( y \right)}\].
question_answer15) For a real number \[x,\,\left[ . \right]\]denotes the greatest integer. Find the value of\[\left[ \frac{1}{2} \right]+\left[ \frac{1}{2}+\frac{1}{100} \right]+\left[ \frac{1}{2}+\frac{2}{100} \right]+....+\left[ \frac{1}{2}+\frac{99}{100} \right]\].
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