Question

Which one of the following is onto function define from R to R.

(A) f(x) = |x|

(B) f(x) = e^-x

(C) f(x) = x³

(D) f(x) = sin x

Answer 1

Answer is  (C)

f(x) = x³

Given, f : R → R and f(x) = x³

Let y ∈ R (co-domain) if possible, then let pre-image of y is x in domain R, then

f(x) = y

⇒ x³ = y

⇒ x = y^1/3 ∈ R ∀ y ∈ R

So, pre-image of each value of y is exist in domain R.

So, R is onto function.