The function is also undefined when the expression under the radical is negative:
So the expression is defined for all x such that x ≤ −2 or x ≥ 2, except x = 4. The answer is (E).
There is a third thing that can result in undefined values in a function: logarithms. Similar to square
roots, the log of a negative number is undefined. Unlike roots, however, the log of 0 is also
undefined. If you keep these three cases in mind, you can determine the total domain of a function
with ease.
INVERSE FUNCTIONS
Perhaps the most advanced functions question you’ll face on Math 2 will be one involving the
inverse of a function—written f−1(x)—as in Example 6.
Example 61. If , then f−1 (x)=(A)(B)(C)