Question

8. If A = {1,3,5,7,9) and B = {2,4,6,8,10,12} define a function f: A+B by f(x) =x + 1, a ∀ x ∈A is the function one - one and onto?​

Answer 1

We can see function is a polynomial and the domain of polynomial function is real number.

∴  x∈R

f(x)=−x2+6x−8

         =−(x2−6x+8)

         =−(x2−6x+9−1)

         =−(x−3)2+1

Maximum value of −(x−3)2 would be 0

∴  Maximum value of −(x−3)2+1 would be 1.

∴  f(x)∈(−∞,1]

We can see from the given graph that function is symmetrical about x=3 and the given function is bijective.

So, x would be either (−∞,3] or [3,∞)

The correct option which satisfy A and B both is:

A=(−∞,3] and B=(−∞,1]