The function defined by is
Onto but not One-One
The explanation for the correct option
Given function, .
Differentiate the given function with respect to .
Factorize the given quadratic expression using the quadratic formula.
Now, for increasing intervals .
Thus, the given function is increasing in nature in and decreasing in nature elsewhere.
Hence, the given function is a Many-One function.
As the given function is a polynomial function, thus it is defined for all real values of and the range is also all real numbers.
Thus, the range is , which is equal to the given co-domain.
So, the given function is an Onto function.
Hence, option B is correct .