If `f(x)a n dg(x)` are two positive and increasing functions, then which of the following is not always true? `[f(x)]^(g(x))` is always increasing `[f(x)]^(g(x))` is decreasing, when `f(x)<1` `[f(x)]^(g(x))` is increasing, then `f(x)> 1.` 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 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) and g(x)=f(x)sqrt(1-2(f(x))^2) are strictly increasing AAx in R , then find the values of f(x)dot

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

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

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).

Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integers. If f(g(20))-g(f(20))=28 , then which of the following is not true? a=15 b. a=6 c. b=14 d. b=3

Let f(x) and g(x) are two differentiable functions. If f(x)=g(x) , then show that f'(x)=g'(x) . Is the converse true ? Justify your answer

If f(x) and g(x) are continuous functions, then int_(In lamda)^(In (1//lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx is

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 intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x)=2x (d) g(x)=x