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Question

If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to

A
11+(g(x)x)2
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B
11(g(x)x)2
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C
12+(g(x)x)2
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D
12(g(x)x)2
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Solution

The correct option is C 12+(g(x)x)2
Let y=f(x)x=f1(y)
then f(x)=x+tanx
x=f1(y)+tan(f1(y))
x=g(y)+tan(g(y)) or x=g(x)+tan(g(x)) (i)
Differentiating both sides, then we get
1=g(x)+sec2g(x).g(x)
g(x)=11+sec2(g(x))=11+1+tan2(g(x))
=12+(xg(x))2 [from Eq.(i)]
12+(g(x)x)2

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