Let f : R → R defined by $f(x)=x^3+x^2+100x+5\sin x$, then f is

many-one onto many-one into one-one onto one-one into

one-one onto

$f(x)=x^3+x^2+100x+5\sin x$ $∴ f'(x) =3x^2+ 2x +100 +5\cos x$ $=3x^2+ 2x +94+(6+5\cos x)>0$ ∴ is an increasing function and consequently a one-one function. Clearly $f(−∞) = −∞, f(∞) = ∞$ and f(x) is continuous, therefore range f = R = codomain f. Hence f is onto.