Question 12
Let* f* : R → R be defined as f(x) = 3x. 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.

Answer

*f*: R → R 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 _{}in **R** such that.

∴*f* is onto.

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

The correct answer is A.