If `f(x)a n dg(x)` are two positive and increasing functions, then which of the following is not always true? (a) `[f(x)]^(g(x))` is always increasing (b) `[f(x)]^(g(x))` is decreasing, when `f(x)<1` (c) `[f(x)]^(g(x))` is increasing, then `f(x)< 1.` (d) If `f(x)>1,t h e n[f(x)]^(g(x))` is increasing.

If fogoh(x) is an increasing function, then which of the following is not possible? (a) f(x),g(x),a n dh(x) are increasing (b) f(x)a n dg(x) are decreasing and h(x) is increasing (c) f(x),g(x),a n dh(x) are decreasing

The function f(x)= tan^(-1) (sin x + cos x ), x gt 0 is always an increasing function on the interval-

Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Statement 2: If both f(x)a n dg(x) are increasing in (a , b),t h e nf(x)g(x) must be increasing in (a,b).

Find the intervals in which the function f given by f(x) = x^(2) – 4x + 6 is (a) increasing (b) decreasing

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing

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.

Let f(x)=(x)/(1+|x|) Interval of increase of f(x) is -

f: R to R ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot Then f(x) is a) always increasing (b) decreasing either increasing or decreasing c) non-monotonic

If f(x)a n dg(x) are periodic functions with periods 7 and 11, respectively, then the period of f(x)=f(x)g(x/5)-g(x)f(x/3) is (a)177 (b) 222 (c) 433 (d) 1155

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in