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

$f(x)=x^3+x^2+100x+5\sin x$

$∴ f'(x) =3x^2+ 2x +100 +5\cos x$

$=3x^2+ 2x +94+(6+5\cos x)>0$

∴ 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.