A function f(x) is defind as
`f(x)={{:(x^(2)+ax+1, " x is rational "),(ax^(2)+2x+b,"x is irrational "):}`
is continuous at x=1and 3 , them find the values of a and b.

if f(x)=x^2-ax+3 , x is rational and f(x)=2-x , x is irrational is continuous at exactly two points, then the possible values of a

Discuss the continuity of function f(x)={{:(1,"if x is rational"),(0,"if x is irrational"):}

Discuss the continuity of f(x)={x^2, x is rational -x^2, x is irrational dot

Let f (x)= {{:(sin ^(2) x"," , "x is rational"),(-sin ^(2)x",", " x is irrational"):}, then set of points, where f (x) is continuous, is:

Let f (x)= {{:(sin ^(2) x"," , "x is rational"),(-sin ^(2)x",", " x is irrational"):}, then set of points, where f (x) is continuous, is:

Let f(x) be given that f(x)={{:(,x,"if x is rational"),(,1-x,"if x is irrational"):} The number of points at which f(x) is continuous, is

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.

If the function f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, x ge 2):} is continuous at x=1 and discontinuous at x=2 , find the values of A and B .

A function f(x) is defined as followings : f(x)={ax-b, x = 2 Prove that if f(x) is continuous at x=1 but discontinuous at x =2. then the locus of the point (a,b) is a straight excluding the point where it cuts the line y=3.

If the function f(x) = axe^(bx^(2)) has maximum value at x=2 such that f(2) =1 , then find the values of a and b