Question

Assertion (A): Let Z be the set of integers. A function f: Z → Z defined as f(x) = 3x − 5. ∀x ∈ Z is a bijective.

Reason (R): A function is a bijective if it is both surjective and injective.

Options

• Both Assertion (A) and Reason (R) are true and the Reason (R) is thecorrect explanation of the Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not thecorrect explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Assertion (A) is false, but Reason (R) is true.

Explanation:

f(x) = 3x − 5 b

for one - one (Injective)

f(x) = f(y)

3x − 5 = 3y − 5

3x = 3y

x = y

∴ f(x) is injective 

Surjective

f(x) = y

3x − 5 = y

3x = y + 5

x = `(y + 5)/3`

For example if y = 1

Then x = `(1 + 5)/3`

= `6/3`

 = 2 (integer) ∈ Z

If y = 2

x = `(2 + 5)/3`

= `7/3`   (not an integer) ∉ Z

∴ f(x) is not surjective.

Hence, f(x) is not bijective.