Problem 12 Solution

This page contains the NCERT mathematics class 12 chapter Relations and Functions Exercise 1.2 Problem 12 Solution. Solutions for other problems are available at Exercise 1.2 Solutions
Exercise 1.2 Problem 12 Solution
12. Let f : R → R be defined as {f(x) = 3x}. Choose the correct answer.
f is one-one onto
f is many-one onto
f is one-one but not onto
f is neither one-one nor onto.
To Check whether f is one-one:
Consider two elements x_1, x_2R 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 yR in the co-domain should be an image of some element xR 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.