JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\) and \(g\) be differentiable functions on \(\mathrm{R}\) such that \(fog\) is the identity function. If for some \(a, b \in \mathrm{R}, g^{\prime}(a)=5\) and \(g(a)=b,\) then \(f^{\prime}(b)\) is equal to
- A \(\frac{2}{5}\)
- B \(1\)
- C \(\frac{1}{5}\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
\(f(g(x))=x\) \(f^{\prime}(g(x)) g^{\prime}(x)=1\) put \(x=a\) \(\Rightarrow f^{\prime}(b) g^{\prime}(a)=1\) \(f^{\prime}(b)=\frac{1}{5}\)
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