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CGP EDU Academic Team
Published on: August 14, 2026
If g is inverse of f(x) = x 3 + x + cosx, then find the value of g ′ (1).
Text Solution
Verified by ExpertsThe correct answer is:
1
(1)
Sol. f(g(x)) = x ; f'(g(x)).g'(x) = 1 ⇒ g'(x) = 
x = g(x) 3 + g(x) + cos g(x)
x = 1 ⇒ 1 = g(1) 3 + g(1) + cos g(1) ⇒ g(1) = 0
so g'(1) = 
f'(x) = 3x 2 + 1 – sinx ⇒ f'(0) = 1
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