#### Question

Let *f*: **R** → **R** be defined as *f*(*x*) = 3*x*. Choose the correct answer.

(A) *f* is one-one onto

(B) *f* is many-one onto

(C) *f* is one-one but not onto

(D) *f* is neither one-one nor onto

#### Solution

*f*: **R** → **R** is defined as *f*(*x*) = 3*x*.

Let *x*, *y *∈ **R** such that *f*(*x*) = *f*(*y*).

⇒ 3*x* = 3*y*

⇒ *x* = *y*

∴*f *is one-one.

Also, for any real number (*y)* in co-domain **R**, there exists `y/3` in **R** such that `f(y/3) = 3(y/3) = y`.

∴*f *is onto.

Hence, function *f* is one-one and onto.

The correct answer is A.

Is there an error in this question or solution?

Solution Let F: R → R Be Defined As F(X) = 3x. Choose the Correct Answer. F Is One-one onto (B) F Is Many-one onto F Is One-one but Not onto (D) F Is Neither One-one Nor onto Concept: Types of Functions.