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If (f:\mathbb{R}\to\mathbb{R}) satisfies (f(x+y)=f(x)+f(y)) and (f(1)=3), what is (f(5)), assuming (f) is linear?यदि (f:\mathbb{R}\to\mathbb{R}) ऐसा है कि (f(x+y)=f(x)+f(y)) और (f(1)=3), तो (f(5)) का मान क्या होगा, यदि (f) रैखिक माना जाए?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (15)(15)
Step 1: By the additive property, (f(5)=f(1+1+1+1+1)). Step 2: This becomes (5f(1)=5\cdot3=15). Step 3: In such questions, use repeated addition of the given value.चरण 1: योग गुण के अनुसार (f(5)=f(1+1+1+1+1))। चरण 2: यह (5f(1)=5\cdot3=15) होगा। चरण 3: ऐसे प्रश्नों में दिए हुए मान को बार-बार जोड़कर उपयोग करें।
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