Which of the following function has point of extremum at `x=0?` `f(x)=e^(-|x|)` `f(x)="sin"|x|` `f(x)={x^2+4x+3,x<0-x , xgeq0` `f(x)={|x|,x<0{x},0lt=x<1` (where `{x}` represents fractional part function).

Which of the following function/functions has/have point of inflection? f(x)=x^(6/7) (b) f(x)=x^6 f(x)=cosx+2x (d) f(x)=x|x|

Which of the following function is not differentiable at x=0? f(x)=min{x ,sinx} f(x)={0,xgeq0x^2,x<0 f(x)= x^2 sgn(x)

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

Discuss the extreama of the following functions (i)f(x)=|x|,(ii)f(x)=e^(-|x|),(iii) f(x)=x^(2//3)

Which of the following functions has (have) y-symmetry or origin symmetry? (i) f(x) = x^(2) sin x" "(ii) f(x) = log ((1-x)/(1+x)) (iii) f(x) = x/(e^(x)-1)+x/2 + 1

Which of the following functions has inverse function? a) f: ZrarrZ defined by f(x)=x+2 b) f: ZrarrZ defined by f(x)=2x c) f: ZrarrZ defined byy f(x)=x d) f: ZrarrZ defined by f(x)=|x|

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

Which of the following hold(s) good for the function f(x)=2x-3x^(2/3)? (a) f(x) has two points of extremum. (b) f(x) is convave upward AAx in Rdot (c) f(x) is non-differentiable function. (d) f(x) is continuous function.

Discuss the extremum of f(x)={|x^2-2|, -1lt=x