Let {\X}= \{x^2: x \in \bo {N}\} and the function f: \bo ...

CBSE Class 12 Math 2022 Term I Solved Paper

Question : 27 of 50

Marks: +1, -0

Let

{\X}= \{x^2: x ∈ \bo {N}\}

and the function

f: \bo {N} → {\X}

is defined by

f(x)=x^2, x ∈ {\N}

. Then this function is

Solution: 👈: Video Solution

Explanation: Let

x_1, x_2 ∈ {\N}

f (x_1) \;=f (x_2)

⇒\;x_1^2\;=x_2^2

⇒\;x_1^2-x_2^2\;=0

⇒ \;\; (x_1+x_2) (x_1-x_2) =\;0

⇒ \;\; x_1=\;x_2

\;

Hence,

f(x)

is injective.
Also, the elements like 2 and 3 have no pre-image in N. Thus,

f(x)

is not surjective.

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