यदि f(x) = ln (x + है, तो निम्नलिखित में से कौन-सा सही है ?

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NDA 02/2022 Mathematics Official Paper (Held On 04 Sep 2022)
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  1. f(x) + f(−x) = 0
  2. f(x)−f(−x) = 0
  3. 2f(x) = f(−x)
  4. f(x) = 2f(−x)

Answer (Detailed Solution Below)

Option 1 : f(x) + f(−x) = 0
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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संकल्पना:

  • (x + y)(x - y) = x2 - y2

गणना:

दिया गया हैf(x) = ln (x + ),__(i)

(i) में x को (-x) से प्रतिस्थापित करने पर,

⇒  f(-x) = ln (-x + ),

⇒  f(-x) = ln (-x + ),

ln फलन के अंदर (x + ) से गुणा और भाग करने पर,

⇒  f(-x) =  ,

⇒  f(-x) =  ,

⇒  f(-x) =  ,

⇒  f(-x) =  ,

(i) से,

⇒  f(-x) =  - f(x)\

⇒  f(-x) + f(x) = 0

सही उत्तर विकल्प (1) है।

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