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

Consider the function h(x)=(g^(2)(x))/(2)+3x^(3)-5 , where g(x) is a continuous and differentiable function. It is given that h(x) is a monotonically increasing function and g(0) = 4. Then which of the following is not true ?

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

Function f(x)=|x|-|x-1| is monotonically increasing when x 1 x<1 (d) 0

Prove that f(x)=x-sinx is an increasing function.

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

The function y=2x^2-ln|x| is monotonically increasing for values of x(!=0) satisfying the inequalities____ and monotonically decreasing for values of x satisfying the inequalities_____.

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is monotonically increasing for x in Rdot

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

Is the function defined by f(x)= |x| , a continuous function?

if f(x) =2e^(x) -ae^(-x) +(2a +1) x-3 monotonically increases for AA x in R then the minimum value of 'a' is