Question

The function f:R->R defined by f(x) =(x-a)(x-b)(x-c) where a,b,c included in R
a) not one-one but onto
b)one-one but not onto
c)both one-one and onto
d)neither one-one nor onto

Answer 1

This function is not an one-one function as for x=a,b and c, the functional value is 0. As f(a) = f(b), but a≠b, it is not an one-one function.

It is a unto function as its range is R. For x=-∞, f(x) can be -∞ and for x=∞, f(x) can be ∞. And since it is a continuous function, all the real numbers are its range. 

So the function is not one-one but onto. answer is (a).