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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 27 of 50
Marks: +1, -0
Let X={x2:x∈N}X = \{x^2: x \in \mathbb{N}\} and the function f:N→Xf: \mathbb{N} \rightarrow X is defined by f(x)=x2,x∈Nf(x)=x^2, x \in N. Then this function is
Solution:     👈: Video Solution
Explanation: Let x1,x2∈Nx_1, x_2 \in N
f(x1)  =f(x2)f(x_1) \;= f(x_2)
⇒x12=x22\Rightarrow x_1^2 = x_2^2
⇒x12−x22=0\Rightarrow x_1^2 - x_2^2 = 0
⇒(x1+x2)(x1−x2)=0\Rightarrow (x_1+x_2)(x_1-x_2) = 0
⇒x1=x2\Rightarrow x_1 = x_2
  \;
Hence, f(x)f(x) is injective.
Also, the elements like 2 and 3 have no pre-image in N. Thus, f(x)f(x) is not surjective.
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