Practicing Success
If a real polynomial of degree n satisfies the relation $f(x)=f'(x) f''(x)$ for all $x∈ R$. Then $f: R→ R$ |
an onto function an into function always a one function always a many one function |
an onto function |
The correct answer is Option (1) → an onto function Let f(x) be a polynomial of degree n. Then, f'(x) and f''(x) are polynomials of degree (n-1) and (n-2) respectively. $∴f(x)=f'(x) f''(x)$ for all $x∈ R$ $⇒ deg (f(x)) = deg (f'(x)) + deg (f''(x))$ $⇒n=(n-1)+n-2⇒n=3$ Clearly, f(x), being a polynomial of degree 3, is an onto function. |