Question
If g is the inverse function of f and , what is the value of g'(35)?
Solution
VerifiedStep 1
1 of 2Given that is the inverse of and
The function must be a one-to-one function because its inverse is a function, and only one-to-one functions have inverses that are functions. Since is the inverse of , we have
Thus, we begin by finding the derivative of
Substituting in the equation for the derivative of gives us
Since is the inverse function of we can say that is the value of for which . Thus, we need to solve
Usually we would have to solve this cubic for . but the solution is apparent by inspection. We can see that has to equal .
So, our answer is
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