Question:
Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b \(\in\) R, \(g'(a) = 5\) and \(g(a) = b\), then \(f'(b)\) is equal to :
Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b \(\in\) R, \(g'(a) = 5\) and \(g(a) = b\), then \(f'(b)\) is equal to :
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Differentiate \(f(g(x)) = x\) with the chain rule and put x = a.
Updated On: Nov 5, 2026
- 1
- 5
- \(\frac{2}{5}\)
- \(\frac{1}{5}\)
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The Correct Option is D
Solution and Explanation
\(f(g(x)) = x\) for all x. Differentiating, \(f'(g(x))\,g'(x) = 1\).
At x = a: \(f'(g(a))\,g'(a) = 1\), i.e. \(f'(b) \cdot 5 = 1\).
So \(f'(b) = \frac{1}{5}\).
Answer: (4) \(\frac{1}{5}\)
At x = a: \(f'(g(a))\,g'(a) = 1\), i.e. \(f'(b) \cdot 5 = 1\).
So \(f'(b) = \frac{1}{5}\).
Answer: (4) \(\frac{1}{5}\)
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