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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b) is bijective, what is the necessary condition on (a)?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b) द्वैक है, तो (a) के लिए आवश्यक शर्त क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (a\ne 0)(a\ne 0)
Step 1: If (a=0), then (f(x)=b) becomes constant. Step 2: A constant function is neither one-one nor onto on (\mathbb{R}). Step 3: Therefore a linear function is bijective only when (a\ne 0).चरण 1: यदि (a=0), तो फलन (f(x)=b) स्थिर हो जाएगा। चरण 2: स्थिर फलन न एकैकी होगा और न (\mathbb{R}) पर आच्छादक होगा। चरण 3: इसलिए रैखिक फलन को द्वैक होने के लिए (a\ne 0) चाहिए।
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