Let f and g be differentiable functions on R such that f g is the identity function. If for some a, b R , g'(a) = 5 and g(a) = b , then f'(b) is equal - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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Let f and g be differentiable functions on R such that f \circ g is the identity function. If for some a, b \in R, g^{'} (a) = 5 and g (a) = b, then f^{'} (b) is equal to:

Solution & Step-by-step Explanation

Given f (g (x)) = x (Identity function).Differentiating both sides with respect to x using the chain rule: f^{'} (g (x)) \cdot g^{'} (x) = 1 At x = a : f^{'} (g (a)) \cdot g^{'} (a) = 1 Substitute g (a) = b and g^{'} (a) = 5 : f^{'} (b) \cdot 5 = 1 f^{'} (b) = \frac{1}{5}

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Let f and g be differentiable functions on R such that f \circ g is the identity function. If for some a, b \in R, g^{'} (a) = 5 and g (a) = b, then f^{'} (b) is equal to:

2/5

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1/5

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