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

If f(x) = |(0, x-a, x-b),(x+a, 0, x-c),(x+b, x+c, 0)| , then the value of f(0) is :

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then (a) f is one-one but not onto (b) f is onto but not one-one (c) f is both one-one and onto (d) none of these

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

Locate roots of f'(x) = 0 , where f(x) = (x - a)(x - b)(x -c), a < b < c

If f(x)=(x-1)/(x+1) , then prove that: (f(b)-f(a))/(1+f(b)*f(a))=(b-a)/(1+ab)

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)=(ax+b)/(cx+d) , x!=-d/c . If d=-a, show that f{(x)}=x is an identity.

Let A=R-{3} and B=R-[1]. Consider the function f:A rarr B defined by f(x)=((x-2)/(x-3)). Show that f is one-one and onto and hence find f^(-1)