Question

Classify the following function $f\left(x\right)$ defined in $R\to R$ as injective, surjective, both or none:

$f\left(x\right)=(x^2+x+5)(x^2+x-3)$

• A. Only injective
• B. Only surjective
• C. Neither injective not surjective
• D. Both injective and surjective.

Answer 1

The correct option is C Neither injective not surjective

$f\left(x\right)=(x^2+x+5)(x^2+x-3)$
Clearly given polynomial is bi-quadratic, and we know a polynomial with even degree is neither injective nor surjective.