If `f(x)=|[x+lambda,x,x] , [x,x+lambda,x] , [x,x,x+lambda]|` then `f(12x)-f(x)=`

Let A=[[x+lambda,x,x] , [x,x+lambda,x] ,[x,x,x+lambda]] then A^(-1) exists if (A) x!=0 (B) lambda!=0 (C) 3x+1!=0 , lambda!=0 (D) x!=0 , lambda!=0

|[x+lambda, 2x, 2x], [2x, x+lambda, 2x], [2x, 2x, x+lambda]| =(5x+ lambda)(lambda-x)^(2)

Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}] then prove that A^(-1) exists if 3x+lambda ne0, lambda=ne0

Evaluate the following : |{:(x+lambda,x,x),(x,x+lambda,x),(x,x,x+lambda):}|

If f(x)=(2018x-2019)/(x+lambda) and f(f(x))=x then lambda=

Let f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):} and lambda in R , then at x = 0

If f(x)=lambda|sin x|+lambda^(2)|cos x|+g(lambda) has a period =(pi)/(2) then find the value of lambda

Let f(x)=lambda+mu|x|+nu|x|^(2), where lambda,mu,nu in R, then f'(0) exists if

Let f(x)=(x^(4)-lambdax^(3)-3x^(2)+3lambdax)/(x-lambda). If range of f(x) is the set of entire real numbers, the true set in which lambda lies is

The values of lambda for which the function f(x)=lambda x^(3)-2 lambda x^(2)+(lambda+1)x+3 lambda is increasing through out number line (a) lambda in(-3,3)( b) lambda in(-3,0)( c )lambda in(0,3) (d) lambda in(1,3)