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**NCERT mathematics class 12 chapter Relations and Functions Exercise 1.2 Problem 12 Solution**. Solutions for other problems are available at Exercise 1.2 SolutionsExercise 1.2 Problem 12 Solution

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.

To Check whether f is one-one:

Consider two elements x_1, x_2 ∈ R such that

{f(x_1) = f(x_2)}

⇒ {3x_1 = 3x_2}

⇒ {x_1 = x_2}

∴ f is not one-one.

To Check whether f is onto:

For f to be onto, every element y ∈ R in the co-domain should be an image of some element x ∈ R in the domain, such that

{y = f(x) = 3x}

⇒ x = \dfrac{y}{3}

This mapping will be true for all values of y.

⇒ Every element y in the co-domain will be an image of an element x in the domain.

∴ f is onto.

∴ As f is both one-one and onto, A is the correct answer.