Question

The function \( f:[0,3] \to [1,29] \) defined by \[ f(x) = 2x^3 - 15x^2 + 36x + 1 \] is

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

Hint:

To test if a function is one-to-one, examine if each value in the range corresponds to exactly one value in the domain. For onto, check if every element in the range is mapped to.

Answer 1

The Correct Option is B

The function \( f(x) = 2x^3 - 15x^2 + 36x + 1 \) is analyzed by checking whether it is one-to-one and onto.
After analyzing the function, it is found to be onto but not one-to-one.