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If (f(x)=|x-2|), what is the set (f^{-1}({3}))?यदि (f(x)=|x-2|), तो (f^{-1}({3})) कौन-सा समुच्चय है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({-1,5})({-1,5})
Step 1: For (f^{-1}({3})), solve (|x-2|=3). Step 2: This gives (x-2=3) or (x-2=-3). Step 3: Hence (x=5) or (x=-1), so the preimage is ({-1,5}).चरण 1: (f^{-1}({3})) के लिए (|x-2|=3) हल करें। चरण 2: इससे (x-2=3) या (x-2=-3) मिलता है। चरण 3: इसलिए (x=5) या (x=-1), अतः पूर्वछवि ({-1,5}) है।
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