Let `f: RtoR ,f(x)=(x-a)/((x-b)(x-c)),b > c `
If `f` is onto, then prove that `a in (c , b)`

If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a) , then prove that f(a) + f(b) = a + b.

If f(x)=a(x-b)/(a-b)+b.(x-a)/(b-a) then show that f(a)+f(b)=f(a+b).

Let f:RtoR be defined as f(x)=(x^(2)-x+4)/(x^(2)+x+4) . Then the range of the function f(x) is

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

Let f(x) :R->R,f(x)={(2x+alpha^2,xge2),((alpha x)/2+10,x lt 2)) If f(x) is onto function then alpha belongs to (A) [1,4] (B) [-2,3] (C) [0,3] (D) [2,5]

Let f:RtoR be defined by f(x)=x/(1+x^2),x inR . Then the range of f is

Let f(x)=(ax + b )/(cx+d) . Then the fof (x)=x , provided that : (a!=0, b!= 0, c!=0,d!=0) ; A. d=-a , B. d=a ,C. a=b=c=d=1 ,D. None of these.

If f(x)=a.(x-b)/(a-b)+b.(x-a)/(b-a) , show that, " "f(a)+f(b)=f(a+b) .

Let P(x) equiv ((x-a)(x-b))/((c-a)(c-b)).c^2+((x-b)(x-c))/((a-b)(a-c)).a^2+((x-c)(x-a))/((b-c)(b-a)).b^2 Prove that P(x) has the properly that P(y) = y^2 for all y in R.

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then f is (a) one-one and onto (b) one-one and into (c) many-one and onto (d) many-one and into