Let `f(x)={x+2,-1<=x<0; ` `1,x=0; ` ` x/2,0 < x <= 1` 'Then on [-1,1], this function has (a) minimum value (b) maximum value at ?

Let f(x)={((x-1)^2 sin(1/(x-1))-|x|,; x != 1), (-1,; x=1):} then which one of the following is true?

Statement-1 : Let f(x) = |x^2-1|, x in [-2, 2] => f(-2) = f(2) and hence there must be at least one c in (-2,2) so that f'(c) = 0 , Statement 2: f'(0) = 0 , where f(x) is the function of S_1

Let f(x) = {x-1)^2 sin(1/(x-1)-|x| ,if x!=1 and -1, if x=1 1valued function. Then, the set of pointsf, where f(x) is not differentiable, is .... .

Let f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 Then, f(x) is derivable at x=1 , if a=2 (b) b=1 (c) a=0 (d) a=1//2

Let f(x)=x^2-2x-1 AA xinR Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

Let f(x)=max. {2-x,2,1+x} then int_(-1)^1 f(x)dx= (A) 0 (B) 2 (C) 9/2 (D) none of these

Let f(x)={a x^2+1,x >1 ; x+1/2,x<=1.t h e n ,f(x) is derivable at x=1, if a=2 (b) a=1 (c) a=0 (d) a=1/2

"Let "f(x)=x + (1)/(2x + (1)/(2x + (1)/(2x + .....oo))). Then the value of f(50)cdot f'(50) is -

Let f(x)=x^(2)-x+1, AA x ge (1)/(2) , then the solution of the equation f(x)=f^(-1)(x) is

Let f(x)=x^2+x+1 and g(x)=sinx . Show that fog!=gof .