यदि u = g(t) एवं t = f(x), और g एवं f दोनों ऐकेकी तथा आच्छादक फलन हो तो सत्य कथन है :

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RPSC 2nd Grade Mathematics (Held on 18th Feb 2019) Official Paper
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  1. (f−1og−1)(u) = x
  2. (gof)−1 ≡ g−1of−1
  3. (gof)(x) = x
  4. (gof)−1 u = u

Answer (Detailed Solution Below)

Option 1 : (f−1og−1)(u) = x
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RPSC Senior Grade II (Paper I): Full Test 1
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Detailed Solution

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दिया गया है:

u = g(t) और t = f(x)

संकल्पना:

यदि, \(y=f(x)\)

तब, \(x=f^{-1}(y)\)

गणना:

u = g(t)

⇒ u = g(f(x))u

⇒ g-1(u) = f(x)

f को दाएं पक्ष में भेजने पर 

⇒ f-1(g-1(u)) = x

 (f-1og-1)(u) = x

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