Let `g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot` Then `g(x)` increases in (a)`(1/2,2)` (b) `(4/3,2)` (c)`(0,2)` (d) `(0,4/3)`

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

Let g(x)=f(logx)+f(2-logx)a n df''(x)<0AAx in (0,3)dot Then find the interval in which g(x) increases.

Let g(x)=f(x)+f(1-x) and f''(x)>0AAx in (0,1)dot Find the intervals of increase and decrease of g(x)dot

Let g(x)=f(logx)+f(2-logx) and f^(prime prime)(x)<0AAx in (0,3)dot Then find the interval in which g(x) increases.

Let g(x)=2f(x/2)+f(2-x) and f''(x) < 0 AA x in (0,2). If g(x) increases in (a, b) and decreases in (c, d), then the value of a + b+c+d-2/3 is

Let g(x) = 2 f(x/2)+ f(2-x) and f''(x) lt 0 forall x in (0,2) . Then calculate the interval in which g(x) is increasing.

Let f(x)=(x^(2)-2x+1)/(x+3),f i n d x: (i) f(x) gt 0 (ii) f(x) lt 0

Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical about. (a)The origin (b) the line x=1/2 (c) the point (1,0) (d) the point (1/2,0)

Let varphi(x)=f(x)+f(2a-x) and f"(x)>0 for all x in [0,\ a] . Then, varphi(x) (a) increases on [0,\ a] (b) decreases on [0,\ a] (c) increases on [-a ,\ 0] (d) decreases on [a ,\ 2a]

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot