Lesson25

# Lesson25 - MA 15200 I The Domain of a Function Lesson 25...

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1 MA 15200 Lesson 25 Section 2.6 I The Domain of a Function Remember that the domain is the set of x ’s in a function, or the set of ‘first things’. For many functions, such as ( ) 2 3 f x x = - , x could be replaced with any real number to find ( ) f x . Therefore the domain could be written in set-builder notation as { | is a real number} x x or ( , ) -∞ ∞ using interval notation. However, not all functions have domains that are all real numbers. In real life examples, the domain is often limited to numbers that only make sense. For example, if 50 d t = (distance in miles equals 50 times time in hours), the time can only be 0 or positive numbers. No one would travel negative hours. So the domain would be { | 0} or [0, ) t t . Examine the following two functions. 2 ( ) 4 ( ) 3 f x x g x x = - = - If x is replaced with a 5 in function value for f , the result would be 1 - . While we’ve discussed imaginary numbers, when speaking of domains of functions, we only think of real numbers. So we know 5 is not in the domain of f . How do we find the domain? We know that we can only take the square root of a positive number or zero. Therefore 4 – x must be greater than or equal to zero. 4 0 4 4 x x x - - ≥ - The domain of f is { | 4} or ( ,4] x x -∞ . In function g , if x is replaced with 3, the result would equal 2 0 , which is an undefined number. 3 is not in the domain of function g . We can write the domain as { | is a real number, 3} or ( ,3) (3, ). x x x -∞ The above examples illustrate the ‘problems’ you will encounter possibly when

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Lesson25 - MA 15200 I The Domain of a Function Lesson 25...

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