Which one of the following is onto function define from R to R.(A) f(x

1.	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» 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.

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»

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.