Let `f(x)=(3^(2+x)+3^(2-x))/(3^(2+x)+3^(2-x)-82)`. If m does not belong to the domain of f(x), then integer solutions `(m,n)` of equation `m^(6)+17=n^(2)` are

Let f(x)=x^(2)+3x+2 then number of solutions is

Let f(x)=(x^(2))/(9-x^(2)) and l= number of integers in the domain of f(x) where f(x) is increasing m= number of solutions of f(x)=sin xn= least positive integral value of k for which f(x)=k posses exactly 3 different solutions then

Let f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z . Then

Le t f(x)=(3x^(2)+mx+n)/(x^(2)+1) if range ofthe function is [-10,3) then the value of m-n is -

Let f(x)= [(g(x)-g(-x))/(f(x)+f(-x))]^(m) such that m =2n in N and f(-x) ne -f(x) then f(x) is

Let f(x)=x^3+3/2x^2+3x+3 , then f(x) is

Let f(x)=ln x&g(x)=(x^(4)-x^(3)+3x^(2)-2x+2)/(2x^(2)-2x+3) The domain of f(g(x)) is-

f:R rarr R , f(x)=(3x^(2)+mx+n)/(x^(2)+1) .If the range of this function is [-4,3) , then find the value of m^(2)+n^(2) .