f(x)=x^3 +x.  g(x) = Inverse function of f(x), and; g(29) = 2.  What is the value of g'(2)?Need to get the inverse function correct before differenting. 

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The function `f(x) = x^3 + x` and `g(x) = f^-1(x)` . As g(x) and f(x) are inverse functions `f(g(x)) = x`

=> `(g(x))^3 + g(x) = x`

It is not possible to determine g(x) from the equation obtained above other than by trial and error.

Now, it is given that `g(29) = 2`

=> `g^-1(2) = 29`

=> `f(2) = 29`

But `f(2) = 2^3 + 2 = 8 + 2 = 10` from the definition of f(x).

For `f(x) = x^3 + x` and `g(x) = f^-1(x)` , `g(29)!=2`

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