Science:Math Exam Resources/Courses/MATH110/April 2012/Question 05 (a)

MATH110 April 2012

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Question 05 (a)
Let $\displaystyle f(x)={\frac {2x^{2}}{x^{2}-1}}$ (a) State 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?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Remember that a function is undefined when there is a zero in the denominator of a fraction.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. The numerator and denominator are polynomials, which are defined everywhere. However, since $f(x)$ is a fraction, we need to avoid points where the denominator is zero, i.e. where $x^{2}-1=0$. This occurs when $x=1$ and $x=-1$. So the domain of $f(x)$ is $(-\infty ,-1)\cup (-1,1)\cup (1,\infty )$

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