If `f(x)=|((1+x)^a,(1+2x)^b,1),(1,(1+x)^a,(1+2x)^b), ((1+2x)^b,1,(1+x)^a)|` then find constant term and coefficient of x

If f(x)=|{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x^2-1)):}| then f(100)= ………

If f'(x)=x-(1)/(x^(2)) and f(1)=(1)/(2) then find f(x).

If |{:(x+1,x-1),(x-3,x+2):}|=|{:(4,-1),(1,3):}| then find x

f(x)= {((1)/(2)-x ",",0 le x lt (1)/(2)),(1",",x= (1)/(2)),((3)/(2)-x",",(1)/(2) lt x le 1):} Discuss the continuity of f(x)

Suppose f(x) is a function satisfying the folowing conditions: (i)f(0)=2,f(1)=1 (ii) f(x) has a minimum value at x=(5)/(2) (iii) for all xf'(x)= |{:(2ax,2ax-1,2ax+b+1),(b,b+1,-1),(2(ax+b),2ax+2b+1,2ax+b):}| The number of solutions of the equation f(x) +1=0 is

If |x-1|+|x+1|=2, then find x .

If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c)^3,1]| then f'(x)=lambda|[(x-a)^4,(x-a)^2,1] , [(x-b)^4, (x-b)^2, 1] , [(x-c)^4, (x-c)^2,1]| . Find the value of lambda

f(x)= (1)/((x-1) (x-2)) and g(x)= (1)/(x^(2)) . Find the points of discontinuity of the composite function f(g(x))?

If f(x)=x^(2)," find "(f(1.1)-f(1))/((1.1-1))

If f'(x)=1-(4)/(x^(2)) and f(1)=6 then find f(x) and f(2).