Science:Math Exam Resources/Courses/MATH110/December 2014/Question 01 (a)

MATH110 December 2014

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Question 01 (a)
Give an example of a function whose domain is all real numbers except ${\textstyle x=1}$ and ${\textstyle x=-1}$.

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
Consider rational functions.

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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. Recall that a rational function of the form ${\frac {P(x)}{Q(x)}}$, where $P$ and $Q$ are polynomials, has domain $\{x\in \mathbb {R} :Q(x)\neq 0\}$ Since we want to exclude $x=-1$ and $x=1$, it is enough to find a polynomial $Q$ such that $Q(-1)=Q(1)=0$. The easiest choice of such polynomial is $Q(x)=(x+1)(x-1)$. For the simplicity, if we choose $P(x)=1$, we have $\color {blue}{\frac {1}{(x+1)(x-1)}}$ as a possible answer.