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.
1 Answer | Add Yours
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`
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes