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 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

Which of the follo wing is/are true? f(x)=e^(x) and g(x)=In x, then f(g(x))=x (wherever f(g(x)) is defined )

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

Function f(x),g(x) are defined on [-1,3] and f'(x)>0,g'(x)>0 for all x in[-1,3], then which of the followingis always true?

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

Let f(x)=a(x-x_1)(x-x_2)\ w h e r e\ a ,\ x_1a n d\ x_2\ are real numbers such that a\ !=0\ a n d\ x_1+\ x_2=0. Then which of the following statements is/are always correct? f(x) is increasing in (-oo,0)\ and decreasing in (0,oo) f(x) is decreasing in (-oo,0) and increasing in (0,oo) f(x) is non monotonic on R f(x) has an extremum point

If f and g are two functions defined by f(x)=sqrt(x+1) and g(x)=1/x then find the following functions: f+g

If f and g are two functions defined by f(x)=sqrt(x+1) and g(x)=1/x then find the following functions: f-g

If f and g are two functions defined by f(x)=sqrt(x+1) and g(x)=1/x then find the following functions: f/g

If f^(2)(x)+f(x)=g(x) and g(x) is always increasing then the minimum value that f(x) can attain so that f(x) also increasing is 'k'? Then (2(k+1)) is