Question
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निम्न दो (02) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए :
x और y के सभी वास्तविक मानों के लिए एक फलन इस प्रकार है कि f(xy) = f(x + y) और f(5) = 10 है।
f(0) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
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दिया गया है,
फलन इस प्रकार है कि: x और y के सभी वास्तविक मानों के लिए, \( f(xy) = f(x + y) \) और \( f(5) = 10 \) है।
हमें \( f(0) \) का मान ज्ञात करना है।
दिए गए फलन समीकरण \( f(xy) = f(x + y) \) में \( x = 5 \) और \( y = 0 \) प्रतिस्थापित करने पर:
\( f(5 \cdot 0) = f(5 + 0) \)
\( f(0) = f(5) \)
चूँकि \( f(5) = 10 \), हम निष्कर्ष निकालते हैं:
\( f(0) = 10 \)
इसलिए, सही उत्तर विकल्प 4 है।
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