Question

Let g(x) be the inverse of the function f(x) and f'(x) = `2/(x^2 + 3)`, then 2g'(x) is equal to 

Options

• `1/(3 + ["g"(x)]^2)`

• `1/(3 + ["f"(x)]^2)`

• 3 + [g(x)]²

• 3 + [f(x)]²

Answer 1

3 + [g(x)]²

Explanation:

Since g(x) is the inverse of f(x)

∴ fog(x) = x

`=> "d"/"dx" ["fog" (x)] = "d"/"dx" (x)`

`=> "f'" ["g"(x)]*"g'"(x) = 1`

`=> 2/(["g"(x)]^2 + 3) * "g'"(x) = 1   ....[because "f'"(x) = 2/(x^2 + 3) ("given")]`

⇒ 2g'(x) = 3 + [g(x)]²