`f(x)=|x^2-3|x|+2|dot` Then which of the following is/are true `f^(prime)(x)=2x-3forx in (0,1)uu(2,oo)` `f^(prime)(x)=2x+3forx in (-oo,-2)uu(-1,0)` `f^(prime)(x)=-2x-3forx in (-2,-1)` `non eoft h e s e`

If f:(-oo,3]rarr[7,oo);f(x)=x^(2)-6x+16, then which of the following is true

If f(x)=2x-3, find f(0),f(1),f(-2)andf((x+3)/(2)) .

Consider the function f:(-oo,\ oo)->(-oo,oo) defined by f(x)=(x^2-a x+1)/(x^2+a x+1),\ 0

If f: RvecR is a differentiable function such that f^(prime)(x)>2f(x)fora l lxRa n df(0)=1,t h e n : f(x) is decreasing in (0,oo) f^(prime)(x) e^(2x)in(0,oo)

Function f(x)=x^(2)(x-2)^(2) is (A) increasing in (0,1)uu(2,oo)

Let f(x)=a(x-x_1)(x-x_2)\ w h e r e\ a ,\ x_1a n d\ x_2\ are real numbers such that a\ !=0\ a n d\ x_1+\ x_2=0. Then which of the following statements is/are always correct? f(x) is increasing in (-oo,0)\ and decreasing in (0,oo) f(x) is decreasing in (-oo,0) and increasing in (0,oo) f(x) is non monotonic on R f(x) has an extremum point

The domain of the function f :R rarr R defined by f(x)=sqrt(x^(2)-3x+2) is (-oo,a]uu[b,oo) then a+ b=

The domain of the function f:R rarr R defined by f(x)=sqrt(x^(2)-3x+2) is (-oo,a]uu[b,oo) then b-a

Solve forx :(x+1)/(x-1)+(x-2)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2

The domain of the function f(x)=((x+1)(x-3))/(x-2) is [-1,2)uu[3,oo) b. (-oo,-3)uu(2,5) c. (-oo,-3]uu[2,5] d. none of these