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 g(x)=2f(x/2)+f(x) and f''(x)lt0 " in "0lexle1 , then g(x)

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. if both the statements are true and statement 2 is the correct explanation of statement 1. If both the statements are true but statement 2 is not the correct explanation of statement 1. If statement is True and statement 2 is false. If statement1 is false and statement2 is true. Statement 1 : If g(x)=f(x)-1,f(x)+f(1-x)=2AA x in R , then g(x) is symmetrical about the point (1/2,0)dot Statement 2 : If g(a-x)=-g(a+x)AAx in R , then g(x) is symmetrical about the point (a ,0)

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

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

If |f(x_2)-f(x_1)|le(x_2-x_1)^2AAx_1,x_2inR, then the equation of tangent to the curve y = f(x) at the point (1,2) is

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

If f(x)=x+1,g(x)=x^2+1 , then (f+g)/(fg) (0) =?

f(x)=e^x.g(x) , g(0)=2 and g'(0)=1 then f'(0)=

If f(x) is a real-valued function defined as f(x)=In (1-sinx), then the graph of f(x) is (A) symmetric about the line x =pi (B) symmetric about the y-axis (C) symmetric and the line x=(pi)/(2) (D) symmetric about the origin

If f(x)=3x+1,g(x)=x^3+2 , then (f+g)/(fg) (0) =?