Question

check the symmetry f(x)=x^3+5x+1​

Answer 1

Solution:

Given that f(x)=x3+5x+1

∴f′(x)=3x2+5>0,∀x∈R

⇒f(x) is strictly increasing on R

⇒f(x) is one one

∴ Being a polynomial f (x) is continuous and increasing.

on R with limx→∞f(x)=−∞ and limx→∞f(x)=∞

∴ Range of f=(−∞,∞)=R

Hence f is onto also. So, f is one one and onto R.