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State with Reasons Whether the Following Functions Have Inverse : G : {5, 6, 7, 8} → {1, 2, 3, 4} With G = {(5, 4), (6, 3), (7, 4), (8, 2)}

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प्रश्न

State with reason whether the following functions have inverse :

g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}

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उत्तर

 g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}
(5) = (7) = 4

⇒ f is not one-one.

⇒ f is not a bijection.
So, f does not have an inverse.

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अध्याय 2: Functions - Exercise 2.4 [पृष्ठ ६८]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 2 Functions
Exercise 2.4 | Q 1.2 | पृष्ठ ६८

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