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  4. The function f: R → R defined by f (x) = (x - 1) (x - 2) (x - 3) is

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Q. The function f : R → R defined by f (x) = (x - 1) (x - 2) (x - 3) is

Relations and Functions - Part 2

Solution:

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.