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Question
Choose the correct option from the given alternatives :
If g is the inverse of function f and f'(x) = `(1)/(1 + x)`, then the value of g'(x) is equal to :
Options
1 + x7
`(1)/(1 + [g(x)]^7`
1 + [g(x)]7
7x6
Solution
1 + [g(x)]7
[Hint : Since g is the inverse of f, f–1(x) = g(x)
∴ f[f–1(x)] = f[g(x)] = x
∴ `f'[g(x)]."d"/"dx"[g(x)]` = 1
∴ f'[g(x)] x g'(x) = 1
∴ g'(x) = `(1)/(f'[g(x)]), "where"f'(x) = (1)/(1 + x^7)`
∴ g'(x) = 1 + [g(x)7].
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