R,x!=0,-4<=x<=4}" and "f:A rarr R" is defend by "f(x)=(|x|)/(2)" for "x in

Solve each of the following system of equation in R:2x+6>=0,4x-7<0

If the quadratic equations ax^(2)+bx+c=0(a,b,c epsilon R, a !=0) and x^(2)+4x+5=0 have a common root, then a,b,c must satisfy the relations

Let A={x in R : x ne 0, -4le xle4} and f:A rarrR is defined by f(x)=(|x|)/(x) for x in A. Then the range of f is

If 3x - 2y + 6 = 0, R(x) = 4, then R(y) is

Let f_1:R→R,f_2:[0,∞)→R, f_3:R→R and f_4:R→[0,∞) be defined by f_1(x)={ ∣x∣ if x<0 ; e^x if x≥0 ; f_2(x)=x^2 ; f_3(x)={ sin x if x<0 ; x if x≥0 ; f_4(x)={ f_2(f_1(x)) if x<0 f_2(f_1(x)) if x≥0 ​then f_4 is

IF z=x +iy,x,y, in R, (x,y) ne (0,-4) and Arg ((2z-3)/(z+4i))=pi/4 , then the locus of z is

If f(x)=(4+x)^(n),"n" epsilonN and f^(r)(0) represents the r^(th) derivative of f(x) at x=0 , then the value of sum_(r=0)^(oo)((f^(r)(0)))/(r!) is equal to

If f(x)=(4+x)^(n),"n" epsilonN and f^(r)(0) represents the r^(th) derivative of f(x) at x=0 , then the value of sum_(r=0)^(oo)((f^(r)(0)))/(r!) is equal to

A function f :R to R is given by f (x) = {{:(x ^(4) (2+ sin ""(1)/(x)), x ne0),(0, x=0):}, then