Practice Restricted Domain in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Restricting a domain limits allowable inputs so a function has desired properties, often invertibility.
You keep only the input interval where the function behaves one way.
Example 1
easyFind the natural (implied) domain of f(x) = \sqrt{x - 3}.
Example 2
mediumRestrict the domain of f(x) = x^2 so that the function has an inverse. Find the inverse on this restricted domain.
Example 3
mediumFind the domain of g(x) = \frac{\sqrt{x+4}}{x^2 - 9}.
Example 4
hardRestrict the domain of f(x) = (x - 1)^2 + 3 to the largest interval containing x = 4 on which f is one-to-one, then find f^{-1}(x).