Question

For real x, let f (x) = x^3 + 5x + 1,​

Answer 1

We have,

f(x) = x3 + 5x +1

Therefore, f '(x) = 3x2 + 5 > 0 ∀ x ∈ R

⇒ f(x) is strictly increasing function.

Therefore, f(x) is one-one.

Again, f(x) is continuous function and it is increasing on R.

Therefore, f(x) takes every value between -∞ and ∞.

Thus f(x) is onto.

Hence, the given function f(x) is one-one and onto.