Definition of strictly increasing function #shorts

Strictly increasing functions and strictly decreasing functions

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

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

Prove that the exponential function is strictly increasing on R.

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

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

Show that the function f(x)=x^(2) is strictly increasing function on [0,oo)

In case of strictly decreasing function, the derivative is

Prove that the logarithmic function is strictly increasing on (0,oo)

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)