Learning Resources

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

1. The right half of the parabola; the values of x that are greater than or equal to zero.
2. If you had not used only the principal square root when graphing , you would again have a sideways parabola failing the Vertical Line Test. This would not be a function. Also, since the domain of f(x) is restricted to x 0, the range of f ^-1(x) must be {y / y 0}. Taking only the principal square root results in these desired y-values.
3. The square root of a linear function is the inverse of a quadratic function if the domain of the quadratic function is suitably restricted. You will examine what constitutes a suitable restriction in Focus H.