Which of the following function is surjective but not injective?

$f(x) =x^4+2x^3-x^2+1$ is polynomial of even degree hence its range can’t be R.

Hence not surjective.

$f(x) =x^3+x+1,f'(x)=3x^2+1$ ⇒ monotonic hence bijective.

$f(x) =\sqrt{1+x^2}$, neither surjective not injective.

$f(x) =x^3+2x^2-x+1,\,f'(x)=3x^2+4x-1⇒D=16+12>0$

Hence ( )x f is non-monotonic cubic polynomial hence surjective but not injective.