[" 15.Let "f:R rarr R,f(x)=(x-a)/((x-b)(x-c)),b>c." If "f" is onto,"],[" then prove that "a in(b,c).]

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

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

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)=y=(alphax-b)/(c x-a), AA x in R -{a/c} & a^(2) ne bc then prove that f(y)=x

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)

Prove that f:R rarr R, given by f(x)=2x, is one-one and onto.

Let f:R rarr B be a functio defined by f(x)=tan^(-1).(2x)/(1+x^(2)) , then f is both one - one and onto when B is in the interval

Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval

Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval

The function f:R rarr R defined as f(x)=(3x^2+3x-4)/(3+3x-4x^2) is : (a) One to one but not onto (b) Onto but not one to one (c) Both one to one and onto (d)Neither one to one nor onto