Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x) = x + tan x and f is inverse of g then g'(x) is equal to
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
C
So that we can write f –1 (y) = g(y)
Now f(x) = x + tan x
Put x = f –1 (y)
f(f –1 y) = f –1 (y) + tan (f –1 y)
y = g(y) + tan g(y)
y ⇒ x
x = g(x) + tan g(x) ...(1)
Diff. the function
1 = g'(x) + sec 2 g(x) . g'(x)
g'(x) = 
= 
from equation (1) tan g(x) = [x – g(x)]
sec 2 g(x) = 1 + tan 2 g(x)
= 1 + [x – g(x)) 2
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