
2-6 Calculus – Differentiation and Integration
Example 2.5 Find the domain of each of the following functions for real values:
a. f x x( ) log( ),= −
2
9
b. f x e
x
( ) ,
( )
=
−4
c. f x x( ) = 2sin( 1).-
Solution:
a. Given f x x( ) log( ).= −
2
9
The expression x
2
- 9 must be positive for the function to be real valued. Hence, we need to solve
x
2
- 9 > 0.
The above inequality can be solved by first factoring the left side:
(x - 3)(x + 3) > 0.
Thus, x > 3 or -3. Therefore, the domain of f is given by (-¥, -3) È (3, +¥).
b. Given f x e
x
( ) = .
( )-4
The expression (x - 4) can take any real value and therefore the domain of f is the set of all real
numbers ...