Question
Download Solution PDFf(x) = |x + 1| के रूप में परिभाषित फलन f: R → R+ के संबंध में निम्नलिखित में से कौन सा सही है?
Answer (Detailed Solution Below)
Detailed Solution
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दिया हुआ है कि,
⇒ f(x) = |x + 1|
पहला विकल्प
⇒ f(x2) = |x2 + 1|
⇒ f(x)2 = |x + 1|2
तो हम कह सकते हैं कि
⇒ f(x2) = |f(x)|2
⇒ |x + 1|2 ≠ |x2 + 1|
पहला विकल्प सही नहीं।
दूसरा विकल्प,
⇒ f(|x|) = |f(x)|
⇒ f(|x|) = ||x| + 1|
⇒ |f(x)| = ||x + 1|| = |x + 1|
f(|x|) ≠ |f(x)| क्योंकि x के वास्तविक मूल्यों के लिए ||x| + 1| ≠ |x + 1|।
तीसरा विकल्प,
⇒ f(x + y) = f(X) + f(y)
⇒ f(x + y) = |(x + y) + 1|
⇒ f(y) = |y + 1|
इसलिए
⇒ |(x + y) + 1| ≠ |x + 1| + |y + 1|
इसलिए f(x + y) ≠ f(x) + f(y)Last updated on Jun 18, 2025
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