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

It the graph of the function y=f (x) is symmetrical about the line x=2, then which of the following is correct ?

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

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 the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetric about y-axis, then n equals

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

If f: R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) none of these

Let f(x)=log(2x-x^2)+sin((pix)/2)dot Then which of the following is/are true? (a) Graph of f is symmetrical about the line x=1 (b) Maximum value of f is1. (c) Absolute minimum value of f does not exist. (d) none of these

Given the function f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+f(x-y)= (A) 2f(x).f(y) (B) f(x).f(y) (C) f(x)/f(y) (D) none of these