Value of largest possible `x` for which `5x=7[x]` is

Let f:R to [1,oo),f(x)=x^(2)-4x+5 . Then find the largest possible intervals for which f^(-1)(x) is defined and find corresponding f^(-1)(x).

Let f (x) =x ^(3) + 6x ^(2) + ax +2, if (-3, -1) is the largest possible interval for which f (x) is decreasing function, then a=

If sin(sin x+cos x)=cos(cos x-sin x) then the largest possible value of sin x, is

" If "f(x)=x^((1)/(log x))" ,then set of all possible values of "x" for which "f'(x)=0" is "

The largest set of real values of x for which ln(1+x)<=x is

A rectangle has its sides of lengths sin x and cos x for some x. Largest possible area which it can have,is

The largest set of real values of x for which f(x)=sqrt((x+2)(5-x))-(1)/(sqrt(x^(2)-4))- is a real function is

Let x,y,z in R be such that x+y+z=5 and xy+zy+zx=3 the largest possible value of 'x' is

If sin(sin x+cos x)=cos(cos x-sin x), and largest possible value of sin xis(pi)/(k), then the value of k is