Which one of the following statements does not hold good for the function `f (x) = cos^-1 (2x^2-1) ?`

Range of the function f(x)=(cos^(-1)abs(1-x^(2))) is

Given f(x)={3-[cot^(-1)((2x^3-3)/(x^2))]forx >0{x^2}cos(e^(1/x))forx<0 (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good? f(0^-)=0 b. f(0^+)=3 c. if f(0)=0 , then f(x) is continuous at x=0 d. irremovable discontinuity of f at x=0

For the cubic function f(x)=2x^(3)+9x^(2)+12x+1, which one of the following statement/statements hold good? f(x) is non-monotonic.f(x) increases in (-oo,-2)uu(-1,oo) and decreases in (-2,-1)f:R rarr R is bijective.Inflection point occurs at x=-(3)/(2) .

The domain of the function f(x)=cos^(-1)[log_(2)(x/2)] is

Integrate the function f(x)=(sin x)/(1+cos^2x)