Question

The function f : R $\to$ R defined by f (x) = (x - 1) (x - 2) (x - 3) is

• A. one-one but not onto
• B. onto but not one-one
• C. both one-one and onto
• D. neither one-one nor onto

Answer 1

Answer: (B)

In the function f (x) = (x - 1) (x - 2) (x - 3) for more than one value of x, i.e. x = 1, x = 2 and x = 3, value of the function is zero.
So, the function is not one-one.
Range of the function is the set of all real number i.e. R.
Since Range = Co-domain = R the function is onto.
Thus the given function f(x) is onto but not one-one.