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.

Show that f(x)=1/(1+x^2) is neither increasing nor decreasing on R .

Find the intervals in which f(x)=x|x|,\ \ x in R 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 .

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

Show that the function f(x)=x^2 is neither strictly increasing nor strictly decreasing on R .

The function f(x)=tan^(-1)x-x is decreasing on the set

The function f(x)=x^2-x+1 is increasing and decreasing in the intervals

let f (x) = sin ^(-1) ((2g (x))/(1+g (x)^(2))), then which are correct ? (i) f (x) is decreasing if g (x) is increasig and |g (x) gt 1 (ii) f (x) is an increasing function if g (x) is increasing and |g (x) |le 1 (iii) f (x) is decreasing function if f(x) is decreasing and |g (x) | gt 1

The function f(x) = tan ^(-1)x -x decreases in the interval