If `o+` is an operation such that `a+b={2a ,\ \ \ \ w h e n\ a > b a+b ,\ \ \ \ \ \ \ w h e n\ a

Discuss the applicability of Rolles theorem on the function f(x)={x^2+1,\ \ \ \ w h e n\ 0lt=xlt=1 3-x ,\ \ \ \ w h e n\ 1

Show that f(x)={(|x-a|)/(x-a),\ \ \ w h e n\ x!=a \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \,\ \ \ w h e n\ x=a is discontinuous at x=a for any value of f(a)

Show that f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \2,\ \ \ w h e n\ x=0 is discontinuous at x=0 .

A function f from the set of natural numbers to the set of integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d; -n/2,\ w h e n\ n\ i s\ e v e n (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

A function f from the set of natural numbers to integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d-n/2,\ w h e n\ n\ i s\ e v e n is (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

If x=a+b i is a complex number such that x^2=3+4i and x^3=2+1i ,w h e r e i= sqrt(-1) ,t h e n(a+b) equal to ______.

Let A and B be two sets such that n(A)=3\ a n d\ n(B)=2. if\ (x ,1),\ (y ,2),\ (z ,1)a r e\ in\ AxxB ,\ find \ A\ a n d\ B ,\ w h e r e\ x , y , z are distinct elements.

The scalars la n dm such that l vec a+m vec b= vec c ,w h e r e vec a , vec ba n d vec c are given vectors, are equal to

If x=a+b i is a complex number such that x^2=3+4i and x^3=2+11i ,w h e r e i=sqrt(-1),t h e n (a+b) equal to ______.

If x=a+b i is a complex number such that x^2=3+4i and x^3=2+1i ,w h e r e i=sqrt(-1),t h e n(a+b) equal to ______.