Let f : R → R 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

Solution:

A function f: X → Y is called an onto function if the range of f is Y.

In other words, if each y ∈ Y there exists at least one x ∈ X such that  f(X) = Y,

then f is an onto function.

f : R → R defined as f (x) = 3x

x, y ∈ R such that f (x) = f (y)

⇒ 3x = 3y

⇒ x = y

Therefore,

f is one-one.

For any real number y in codomain R,

there exist y/3 in R such that

f (y/3) = 3 (y/3) = y

Therefore,

f is onto.

Hence, function f is one-one and onto.

The correct answer is A

---

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.2 Question 12

Let f : R → R 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

Summary:

For the function f: R → R defined as f (x) = 3x, we have shown that the function f is one-one onto. Hence the correct answer is A