Let `f(x) = tan^-1 (g(x))`, where `g (x)` is monotonically increasing for `0 < x < pi/2.`

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

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

Let f(x)=cot^-1g(x)] where g(x) is an increasing function on the interval (0,pi) Then f(x) is

Let f(x)=cot^-1g(x)] where g(x) is an increasing function on the interval (0,pi) Then f(x) is

f(x)=x+(1)/(x),x!=0 is monotonic increasing when

Let f and g be two differentiable functions defined on an interval I such that f(x)>=0 and g(x)<= 0 for all x in I and f is strictly decreasing on I while g is strictly increasing on I then (A) the product function fg is strictly increasing on I (B) the product function fg is strictly decreasing on I (C) fog(x) is monotonically increasing on I (D) fog (x) is monotonically decreasing on I

Let f and g be two differentiable functions defined on an interval I such that f(x)>=0 and g(x)<= 0 for all x in I and f is strictly decreasing on I while g is strictly increasing on I then (A) the product function fg is strictly increasing on I (B) the product function fg is strictly decreasing on I (C) fog(x) is monotonically increasing on I (D) fog (x) is monotonically decreasing on I

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.

Let f(x)={x^(2);x>=0ax;x<0 Find real values of a such that f(x) is strictly monotonically increasing at x=0

Let g(x) = f(x) + f(1-x) and f''(x) gt 0, AA x in (0, 1) . Then g(x) a)monotonically decreases in (0, 1). b)monotonically increases in (0, 1). c)non-monotonic and increases in (0, 1/2). d)non-monotonic and decreases in (0, 1/2).