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If \(f:[0,\pi]\to[-1,1]\) and \(f(x)=\sin x\), what is the correct statement about (f)?यदि \(f:[0,\pi]\to[-1,1]\) तथा \(f(x)=\sin x\) है, तो (f) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f) is not one-one because \(f\left(\frac{\pi}{6}\right)=f\left(\frac{5\pi}{6}\right)\)(f) एक-एक नहीं है क्योंकि \(f\left(\frac{\pi}{6}\right)=f\left(\frac{5\pi}{6}\right)\)
Step 1: On \([0,\pi]\), (\sin x) first increases and then decreases. Step 2: \(\sin\frac{\pi}{6}=\frac{1}{2}\) and \(\sin\frac{5\pi}{6}=\frac{1}{2}\), while the angles are different. Step 3: For trigonometric functions check the interval carefully.चरण 1: \([0,\pi]\) पर (\sin x) पहले बढ़ता है फिर घटता है। चरण 2: \(\sin\frac{\pi}{6}=\frac{1}{2}\) और \(\sin\frac{5\pi}{6}=\frac{1}{2}\), जबकि दोनों कोण अलग हैं। चरण 3: त्रिकोणमितीय फलन में अंतराल बहुत ध्यान से देखें।
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