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If \(f:\mathbb{R}\to(0,\infty)\) and \(f(x)=\left(\frac{1}{2}\right)^x\), which statement about (f) is correct?यदि \(f:\mathbb{R}\to(0,\infty)\) तथा \(f(x)=\left(\frac{1}{2}\right)^x\) हो तो (f) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneयह एकैकी है
Step 1: \(\left(\frac{1}{2}\right)^x\) is a decreasing exponential function. Step 2: A decreasing function does not give the same value for two different inputs. Step 3: An exponential function with base between (0) and (1) is also one-one.चरण 1: \(\left(\frac{1}{2}\right)^x\) घटने वाला घातीय फलन है। चरण 2: घटते हुए फलन में दो अलग आगत समान मान नहीं देते। चरण 3: (0) और (1) के बीच आधार वाला घातीय फलन भी एकैकी होता है।
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