Let `f:[0,4 pi]rarr[0,pi]` be defined by `f(x)=cos^(-1)(cos x)` then number of solution of equation `10(1-f(x))=x` when `x in[0,4 pi]` are

Let f:[0,4 pi]rarr[0,pi] be defined by f(x)=cos^(-1)(cos x). The number of points x in[0,4 pi]4 satisfying the equation f(x)=(10-x)/(10) is

Let f:(0,oo)rarr R defined by f(x)=x+9(pi^(2))/(x)+cos x then the range of f(x)

Let f:R rarr(0,(pi)/(6)] be defined as f(x)=sin^(-1)((4)/(4x^(2)-12x+17)) then f(x)

Let F:[3,infty]to[1,infty] be defined by f(x)=pi^(x(x-3) , if f^(-1)(x) is inverse of f(x) then the number of solution of the equation f(x)=f^(-1)(x) are

Let a function f:(1, oo)rarr(0, oo) be defined by f(x)=|1-(1)/(x)| . Then f is

Let f:R rarr[0,(pi)/(2)) defined by f(x)=Tan^(-1)(x^(2)+x+a) then the set of values of a for which f is onto is

Let f:R rarr [0, (pi)/(2)) be a function defined by f(x)=tan^(-1)(x^(2)+x+a) . If f is onto, then a is equal to

Let f: [0,(pi)/(2)]rarr R be a function defined by f(x)=max{sin x, cos x,(3)/(4)} ,then number of points where f(x) in non-differentiable is

Number of solutions of the equation (1+x^(2))cos ecx-4cos^(2)x+1=0 if x in[-2 pi,2 pi], is