SOLUTION: Suppose f(x) = 2^(x^2) - 5, for x >=0. find f^-1, the inverse of f. Determine the domain of f^-1. compute f^(-11).

Algebra ->  Inverses -> SOLUTION: Suppose f(x) = 2^(x^2) - 5, for x >=0. find f^-1, the inverse of f. Determine the domain of f^-1. compute f^(-11).      Log On


   

Question 447941: Suppose f(x) = 2^(x^2) - 5, for x >=0.
find f^-1, the inverse of f. Determine the domain of f^-1.
compute f^(-11).
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that y=2%5E%28x%5E2%29-5, solve this equation for x:y-5=2%5E%28x%5E2%29=>
ln%28y-5%29=x%5E2%2Aln2=>x=sqrt%28ln%28y-5%29%2Fln2%29, interchange x and y and get the
inverse function:f%5E-1%28x%29=sqrt%28ln%28x-5%29%2Fln2%29. The domain of this function is:
(5, infinity). The value x=-11 is not included in its domain for this value
the function f%5E-1%28x%29 is undefined.