Given f(x)=x3+5x+1 Now f′(x)=3x2+5>0,∀x∈R ∴f(x) is strictly increasing function ∴ It is one-one Clearly, f(x) is a continuous function and also increasing on R, Ltx→−∞f(x)=−∞ and Ltx→∞f(x)=∞ ∴f(x) takes every value between −∞ and ∞. Thus, f(x) is onto function.