If `f(x)={[x^(2)-2x(k+1)+2,x geq1],[x-1,x<1]},` is continuous and differentiable,then the value of `k` is

If f(x)=|[1,2(x-1),3(x-1)(x-2)],[x-1,(x-1)(x-2),(x-1)(x-2)(x-3)],[x,x(x-1),x(x-1)(x-2)]| . Then, the value of f(2020) is

If f(x)=x^2+2x+1 , then: f(x-1)-=

If f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s an even function (b) an odd function a periodic function (d) none of these

If f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]

Find the domain of f^(prime)(x) if f(x)=[x/(1+|x|)]if\ |x|geq1 , x/(1-|x|)if\ |x|<1 fig

Let f(x) = {((x^(2) -2x -3)/(x + 1)","," when " x != -1),(" k,"," when " x = -1):} If f(x) is continuous at x = -1 then k = ?