If `g(x)` is a decreasing function on `R` and `f(x)=tan^(-1){g(x)}` . State whether `f(x)` is increasing or decreasing on `R` .

State whether f(x)=tanx-x is increasing or decreasing its domain.

State whether f(x)=tan x-x is increasing or decreasing its domain.

State whether the function f(x) = x^3 is increasing or decreasing.

State whether the function f(x) = e^x is increasing or decreasing.

STATEMENT-1: Let f(x) and g(x) be two decreasing function then f(g(x)) must be an increasing function . and STATEMENT-2 : f(g(2)) gt f(g(1)) , where f and g are two decreasing function .

The function f(x) = a^x is strict decreasing on R, If

f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)) . Find the intervals in which f(x) is increasing or decreasing.

STATEMENT-1: Let f(x) and g(s) be two decreasing function then f(g(x)) must be an increasing function . and STATEMENT-2 : f(g(2)) gt f(g(1)) , where f and g are two decreasing function .

Test whether the following function f(x)=2-3x+3x^(2)-x^(3), x in R is increasing or decreasing.

Test whether the function f(x)= x^(3) + 6x^(2) + 12x-5 is increasing or decreasing for all x in R .