Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x) = x + tan x and g(x) is the inverse of f(x), then g'(x) is equal to
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
C
Given, f(x) = x + tan x
⇒ f(f –1 (x)) = f –1 (x) + tan (f –1 (x))
⇒ x = g(x) + tan(g(x)) …(i)
[ g(x) = f –1 (x)]
⇒ 1 = g'(x) + sec 2 (g(x))g'(x)
⇒ g'(x) = 
⇒ g'(x) = 
⇒ g'(x) = 
[from Eq. (i)]
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