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If (f:\mathbb{R}\to\mathbb{R}) satisfies (f(x+y)=f(x)f(y)), (f(0)=1), and (f(x)>0), what is (f(-x))?यदि (f:\mathbb{R}\to\mathbb{R}) ऐसा है कि (f(x+y)=f(x)f(y)), (f(0)=1), और (f(x)>0), तो (f(-x)) किसके बराबर होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{1}{f(x)})(\frac{1}{f(x)})
Step 1: Put (x+(-x)=0). Step 2: Then (f(0)=f(x)f(-x)=1). Step 3: Since (f(x)>0), (f(-x)=\frac{1}{f(x)}).चरण 1: (x+(-x)=0) रखें। चरण 2: (f(0)=f(x)f(-x)=1)। चरण 3: (f(x)>0) होने से (f(-x)=\frac{1}{f(x)}) मिलता है।
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