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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Differentiation

NTA Abhyas 2020 · Mathematics · Differentiation

If f (x) = x^ 3 + 3x + 1 and g(x) is the inverse function of f (x)...

If f(x)=x3+3x+1f \left(x\right) = x^{3} + 3x + 1 and g(x)g\left(x\right) is the inverse function of f(x)f \left(x\right), then the value of g′(5)isequaltog^{'} \left(5\right) is equal to

Options

  1. A33
  2. B13\dfrac{1}{3}
  3. C16\dfrac{1}{6}
  4. D66

Correct answer

C. 16\dfrac{1}{6}

Step-by-step solution

∵f(x),g∵f \left(x\right), g\left(x\right)areinversefunctionofeachother<br/>are inverse function of each other<br />∴g^{'} (f\left(x\right) ) = \dfrac{1}{f^{'}\left(x\right)}<br/>Nowput<br />Now putx = 1; g^{'}\lleft(f\left(1\right)) = \dfrac{1}{f^{'}\left(1\right)}<br />Hence, $g^{'}\left(5\right) = \dfrac{1}{\left(3x^{2} + 3\right)x = 1}=\dfrac{1}{6}$
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