Learning Resources

Investigation 4: The Square-Root Function & Focus H: Irrational Functions and Inverses

1. The domain of  f ^-1(x) is the range of f(x). Thus the correct answer is
   {x / x > 0}.
2. The range of  f ^-1(x) is the domain of the original function. Since f(x) is linear, it has domain {x / x ? R}. Thus, the range of  f ^-1(x) is {y / y ? R}.
3. It might be a good idea to first write the domain and range of f(x). Its domain is {x / x 3} due to the fact that you cannot take the square root of a negative number in the real number system. Its range is {y / y 0} since it is understood that you are to take only the principal square root. Now consider the inverse function,  f ^-1(x). It has domain {x / x 0} and range {y / y 3}.