Find the domain of each function. a) f(x)=\frac{x^2-4}{x^2-5x+6} b) f(x)=\sqrt{9-x^2}

iarc6io 2022-07-20 Answered
Find the domain of each function.
a ) f ( x ) = x 2 4 x 2 5 x + 6 b ) f ( x ) = 9 x 2
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Answers (2)

Kendrick Jacobs
Answered 2022-07-21 Author has 16 answers
a) Consider the function:
f ( x ) = x 2 4 x 2 5 x + 6
This function is not defined for those values of x for which
x 2 5 x + 6 = 0
Solve for x:
x 2 5 x + 6 = 0 x 2 2 x 3 x + 6 = 0 x ( x 2 ) 3 ( x 2 ) = 0 ( x 2 ) ( x 3 ) = 0 x = 2 , 3
Thus the given function is not defined when x=2 and x=3
That is the function is defined for those values of x for which x 2  and  x 3
The domain of the function in set notation is
{ x R | x 2  and  x 3 }
The domain of the function f(x) in interval notation is
( , 2 ) ( 2 , 3 ) ( 3 , )

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Arectemieryf0
Answered 2022-07-22 Author has 3 answers
b) Consider the function:
f ( x ) = 9 x 2
This function is not defined for those values of x for which
6 x 2 < 0 3 2 x 2 < 0 ( 3 + x ) ( 3 x ) < 0 3 + x < 0  and  3 x < 0 x < 3  and  x < 3 x < 3  and  x > 3
The domain of the function in set notation is
{ x R | 3 x 3 }
The domain of the function f(x) in interval notation is [-3,3]

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