मराठी

The Function F : R → R , F ( X ) = X 2(A) Injective but Not Surjective (B) Surjective but Not Injective (C) Injective as Well as Surjective (D) Neither Injective Nor Surjective

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प्रश्न

The function

\[f : R \to R, f\left( x \right) = x^2\]
 

पर्याय

  • injective but not surjective

  • surjective but not injective

  • injective as well as surjective

  • neither injective nor surjective

MCQ
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उत्तर

Injectivity:
Let x and y be any two elements in the domain (R), such that f(x) = f(y). Then,

\[x^2 = y^2 \] 
\[ \Rightarrow x = \pm y\]
So, f is not one-one.
Surjectivity:
\[\text{As} f\left( - 1 \right) = \left( - 1 \right)^2 = 1\] 
\[\text{and} f\left( 1 \right) = 1^2 = 1, \] 
\[f\left( - 1 \right) = f\left( 1 \right)\]
So, both -1 and 1 have the same images.
\[\Rightarrow\] f is not onto.
So, the answer is (d) .
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पाठ 2: Functions - Exercise 2.6 [पृष्ठ ७७]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 2 Functions
Exercise 2.6 | Q 25 | पृष्ठ ७७

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