`f(x)=[x]` is step-up function. Is it a monotonically increasing function for `x in R ?`

f(x)=[x] is a step up function . Is it a strictly increasing function for x in R.

Show that the function f(x) = x -sin x is an increasing function forall x in R .

the function (|x-1|)/x^2 is monotonically decreasing at the point

Show that the function f(x) = 3x + 2 is strictly increasing function on R.

Show that f(x)=[x] , ([] implies greatest integer function ) is increasing function on R.

Let f(x) be and even function in R. If f(x) is monotonically increasing in [2, 6], then

If f(x) is monotonically increasing function for all x in R, such that f''(x)gt0andf^(-1)(x) exists, then prove that (f^(-1)(x_(1))+f^(-1)(x_(2))+f^(-1)(x_(3)))/(3)lt((f^(-1)(x_(1)+x_(2)+x_3))/(3))

If f(x)=x^3+4x^2+ax+5 is a monotonically decreasing function of x in the largest possible interval (-2,-2//3), then the value of a is

Let f(x) =x - tan^(-1)x. Prove that f(x) is monotonically increasing for x in R

Without using the derivative show that the function f(x)=7x-3 is strictly increasing function on R .