If the graph of `y=f(x)` is symmetrical about the lines `x=1a n dx=2,` then which of the following is true? (a)`f(x+1)=f(x)` (b) `f(x+3)=f(x)` (c)`f(x+2)=f(x)` (d) None of these

If the graph of the function y = f(x) is symmetrical about the line x = 2, then

Consider that the graph of y = f(x) is symmetrie about the lines x = 2 and x = 4 then the period of f(x) is

Given f(x) is symmetrical about the line x=1 , then find out the value of 'x' satisfying f(x-1)=f((x)/(x+1))

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)=|f(x)| (d) none of these

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)=|f(x)| (d) none of these

Which of the following functions is the inverse of itself? (a) f(x)=(1-x)/(1+x) (b) f(x)=5^(logx) (c) f(x)=2^(x(x-1)) (d) None of these

If the function f(x) is symmetric about the line x=3 , then the value of the integral I=int_(-2)^(8)(f(x))/(f(x)+f(6-x))dx is

Given the graph of y=f(x) . Draw the graphs of the followin. (a) y=f(1-x) (b) y=-2f(x) (c) y=f(2x) (d) y=1-f(x)

If f(x)=lim_(n->oo)n(x^(1/n)-1),then for x >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

Given the graph of f(x), draw the graph each one of the following functions : (a) y=f(x)+3 " (b) " y= -f(x)+2 (c ) y=f(x+1)-2 " (d) " y= -f(x-1) (e ) y=f(-x) " (f) " y=f(|x|) (g) y=f(1-x)