Let R denote the set of all real numbers and R⁺ denote the set of all positive real numbers. For the subsets A and B of R define f: A B by f(x)=x^2 for x A . Observe the two lists given below

Step-by-step solution

Given, f(x)=-x^2, f: A B where, A and B RR Real No's x A Here, the domain of the function is positive real number only ie, Domain =A R⁺ Example 1,2,3, and B= 1,4,9, Both set have f: A B unique image. But, A= -1,1,2, and B= 1,1,4, In f: A B have not unique image and for Range x^2=y, x= y ie, (Range R⁺ ) In onto function the (Range = Co-domain =B ) ie, (B R⁺ ) So, (A) f is one-one and onto, if A=B=R⁺ (B f is one-one but not onto, if A=R⁺, B=R (C) f is onto but not one-one, if A=R, B=R⁺ (D) f is neither one-one nor on