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`

A function g(x) is defined as g(x) = (1)/(4) f(2x^(2) - 1) + (1)/(2) f(1- x^(2)) and f'(x) is an increasing function. Then g(x) is increasing in the interval

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.

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 .

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Which of the following statement is always true? (a)If f(x) is increasing, then f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

If fogoh(x) is an increasing function, then which of the following is possible? (a) f(x),g(x),a n dh(x) are increasing (b) f(x)a n d h(x) are increasing and g(x) is decreasing (c) f(x),g(x),a n dh(x) are decreasing

If f(x)=(x^2)/(2-2cosx);g(x)=(x^2)/(6x-6sinx) where 0 < x < 1, (A) both 'f' and 'g' are increasing functions (B) 'f' is increasing and 'g' is decreasing functions (C) 'f' is decreasing and 'g' is increasing functions (D) both 'f' and 'g' are decreasing functions