MATH110 April 2011
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Question 08 (a)
Find the domain of ƒ.
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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Where is the function defined? What does that tell you about the argument () of this function?
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The function is defined for all . Therefore, in order for to be defined, we need . If we factor the left side of the inequality, we get
For what values of x is this inequality true?
If or -2, then the left side of the inequality is zero, which is not allowed. So 2 and -2 cannot be part of our domain. Similarly, if or , then the left side of the inequality will be negative, contradicting the inequality. So these values are also excluded from our domain. If we choose we find that the left hand side of the inequality is positive, satisfying the inequality. Thus our domain is , which written in interval notation is .
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