Asked by Daniel
Giving your answer in interval notation, find the domain of the function sqrt(((x+4)(x−4))/((x−7)(x−5)))
Answers
Answered by
Steve
√( ((x+4)(x−4)) / ((x−7)(x−5)) )
First, you need to exclude values which make the denominator zero: 5 and 7
Next, since the domain of √x is x>=0, you need
((x+4)(x−4)) / ((x−7)(x−5)) >= 0
This is true only for
x <= -4, 4<=x<5 and x>7
or
(-∞,-4]U[4,5)U(7,∞)
First, you need to exclude values which make the denominator zero: 5 and 7
Next, since the domain of √x is x>=0, you need
((x+4)(x−4)) / ((x−7)(x−5)) >= 0
This is true only for
x <= -4, 4<=x<5 and x>7
or
(-∞,-4]U[4,5)U(7,∞)
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