For `"x"in(0,3)`
`g(x)=3f(x/3)+f(3-x)` and `f''(x)gt0A"x"in(0,3)`
If `g(x)` is increasing in `(alpha,3)` and decreasing in `(0,alpha)` then find `alpha`

Let g(x)=3f((x)/(3))+f(3-x) and f''(x)>0 for all x in(0,3) . If "g" is decreasing in (0,alpha) and increasing in (alpha,3) ,then 8 alpha is :

Let g(x)=f(log x)+f(2-log x) and f'(x)<0AA x in(0,3) Then find the interval in which g(x) increases.

If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing on

If f(x)=x^((3)/(2))(3x-10),x>=0, then f(x) is increasing in

If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(pi)/(2) ,then g(x) is increasing in

Let g(x)=x^(2)-2x-2 and f(x)=x^(2)+x+alpha . If f(g(x))=0 has no real solution then the set of values of alpha is.

If f(x)=ln(sin x) and g(x)=sin^(-1)(e^(-x)) for all x in(0,pi) and f(g(alpha))=b and (f(g(x))' at x=alpha is a then which is true.

A function f(x) having the following properties, (i) f(x) is continuous except at x=3 (ii) f(x) is differentiable except at x=-2 and x=3 (iii) f(0) =0 lim_(x to 3) f(x) to - oo lim_(x to oo) f(x) =3 , lim_(x to oo) f(x)=0 (iv) f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3) (v) f''(x) gt 0 AA x in (-oo,-2) uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo) Then answer the following questions Find the Maximum possible number of solutions of f(x)=|x|

If f(x)=3x+1 and g(x)=x^(3)+2 then ((f+g)/(f*g))(0) is: