Science:Math Exam Resources/Courses/MATH100/December 2016/Question 09 (a) (ii)

MATH100 December 2016

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Question 09 (a) (ii)
Let $f(x)={\frac {\sqrt {x^{2}-8}}{x-4}}$. (ii) Give all x-intercepts of $f(x)$.

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
An x-intercept of a function $f$ is a solution to the equation $f(x)=0$.

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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 x-intercepts of a function $f$ are the points at which $f$ vanishes. In other words, they are solutions to the equation $f(x)=0$. Since on the domain of the function, the denominator doesn't vanish, we have $f(x)={\frac {\sqrt {x^{2}-8}}{x-4}}=0\iff {\sqrt {x^{2}-8}}=0\iff x^{2}=8\iff x=\pm 2{\sqrt {2}}$. Since both points are in the domain of the given function (see part (a)), the x-intercepts are $\color {blue}x=\pm 2{\sqrt {2}}$.