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

If the graph of y=f(x) is symmetrical about the lines x=1andx=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

Given the function f(x)=(a^(x)+a^(-x))/(2)(wherea>2)dot Then f(x+y)+f(x-y)= (A) 2f(x).f(y) (B) f(x).f(y) (C) (f(x))/(f(y)) (D) none of these

Let f(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)], then (A) (f(x))^2=-I (B) f(x+y)=f(x),f(y) (C) f(x)^-1=f(-x) (D) f(x)^-1=f(x)

If f(x) is differentiable, then the solution of dy+f\'(x)(y-f(x))dx=0 is (A) yf(x)=Ce^(-f(f(x))^2) (B) y+1=f(x)+Ce^(-f(x)) (C) f(x)=Cye^(-y^2/2) (D) none of these

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

Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

If f(x)=cos(log x), then f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]=

If f(x)=cos(log x), then f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]=

A function f:R rarr R satisfies the equation f(x)f(y)-f(xy)=x+y AA x,y in R and f(1)>0, then f(x)f^(-1)(x)=x^(2)-4bf(x)f^(-1)(x)=x^(2)-6c*f(x)f^(-1)(x)=x^(2)-1d none of these

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g'(f(x)) equal.(a) f'(c)( b) (1)/(f'(c)) (c) f(c) (d) none of these