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` the point (1,0) (d) the point `(1/2,0)`

If f(x) =x^(2) -2,g (x) =2x+ 1 then f^(@) 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 statement2 is false. If statement1 is false and statement2 is true. Statement 1 : Ifg(x)=f(x)-1,f(x)+f(1-x)=2AAx in R ,t h e n(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 increase and decrease of g(x)dot

Let f(x+(1)/(x) ) =x^2 +(1)/(x^2) , x ne 0, then f(x) =?

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

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

If (f(x))^(2)xxf((1-x)/(1+x))=64x AAx in D_(f), then The value of f(9//7) is

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

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)