For the function `f(x)\ =\ 1n\ (1-1n\ x)` which of the following do not hold good? (a)increasing in (0,1) and decreasing in `(1, e)` (b) decreasing in (0,1) and increasing in `(1, e)` (c) `x=\ 1` is the critical number for `f\ (x)` .(d) `f` has two asymptotes

For the function f(x)=e^(e^(x))-tan^(-1)x-3=0 which of the following holds good?

For the function f(x) = (e^(1/x) -1)/(e^(1//x) + 1) , x=0 , which of the following is correct .

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

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

the function f(x)=x^2-x+1 is increasing and decreasing

The function f(x)=(log_(e))(x^(3)+sqrt(x^(6)+1)) is of the following types: (a) even and increasing (b) odd and increasing (c) even and decreasing (d) odd and decreasing

If f(x)=xe^(x(x-1)), then f(x) is (a) increasing on [-(1)/(2),1] (b) decreasing on R (c) increasing on R(d) decreasing on [-(1)/(2),1]

Let f''(x)gt0 and phi(x)=f(x)+f(2-x),x in(0,2) be a function then the function phi(x) is (A) increasing in (0,1) and decreasing (1,2) (B) decreasing in (0, 1) and increasing (1,2) (C) increasing in (0, 2) (D) decreasing in (0,2)

1.Prove that the function f(x)=log_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if '0

Prove that the function f(x)=(log)_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo). if '0