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For (f:\mathbb{R}\to\mathbb{R}), (f(x)=3x-7), what conclusion follows from (f(a)=f(b))?फलन (f:\mathbb{R}\to\mathbb{R}), (f(x)=3x-7) के लिए (f(a)=f(b)) से क्या निष्कर्ष मिलेगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a=b\) / (a=b)\(a=b\) / (a=b)
Step 1: Put (f(a)=f(b)), giving (3a-7=3b-7). Step 2: This gives (3a=3b), hence (a=b). Step 3: If (f(a)=f(b)\Rightarrow a=b), the function is one-one.चरण 1: (f(a)=f(b)) रखने पर (3a-7=3b-7) मिलता है। चरण 2: इससे (3a=3b), इसलिए (a=b)। चरण 3: (f(a)=f(b)\Rightarrow a=b) सिद्ध हो जाए, तो फलन एकैकी होता है।
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