Science:Math Exam Resources/Courses/MATH110/December 2010/Question 09 (a)

MATH110 December 2010

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Question 09 (a)
Let $f(x)={\frac {x+1}{x-1}}$. State the domain of $\displaystyle f$.

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
A function is undefined if it has a zero in the denominator.

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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 domain of a function is the set of all values where the function is defined. The function $f(x)={\frac {x+1}{x-1}}$ is defined everywhere except where its denominator is equal to zero. Setting the denominator equal to zero and solving... $\displaystyle x-1=0$ gives that the denominator is zero when $x=1$. Thus $f(x)$ is defined everywhere except $x=1$. In interval notation this is written $(-\infty ,1)\cup (1,\infty )$, or, equivalently $(-\infty ,\infty )\backslash \{1\}$

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