A weird domain and range? anybody up for a challenge

In summary, the conversation discusses a difficult domain and range problem involving a function with the equation y=x^2-2x+1 / x^2-x-2. The suggested domain is (-infinity,-1) union (-1,2) union (2,infinity) while the range is (-infinity,0) union (-1,infinity). Suggestions are given to possibly rewrite the domain and range in a simpler format, but it is noted that the range may require differentiation to determine its minimum values. The final conclusion is that the suggested domain and range are correct, with the exception of values in the domain (0,8/9).
  • #1
dagg3r
67
0
A weird domain and range? anybody up for a challenge

y=x^2-2x+1 / x^2-x-2

try it on the gfx calculator and check if this domain and range is right

i wrote

Domain ( -infinity, -1 ) union (-1,2) union ( 2, infinity)

range (-infity, 0) union (-1 to infity)

is there an easier way to write the domain and range instead of this format that's assuming this is even right heh please englighten me thanks
 
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  • #2
Is that a typo on your range?
 
  • #3
Domain is correct, you can rewrite it as [itex]\{ x \in \mathbb{R} \ | \ 2 \neq x \neq -1\}[/itex] if you want.

Range is harder... you're going to need to differentiate it to see where it has minima. I get

[tex] \biggr\{ y \in \mathbb{R} \ \biggr| \ y \leq 0 \ \mbox{or} \ y \geq \frac{8}{9}\biggr\}[/tex]
 
Last edited:
  • #4
It is correct.The function doesn't have values in the domain [itex] \left(0,\frac{8}{9}\right) [/itex]

[itex] \mathcal{R}\left( y\right)=\mathbb{R}\diagdown \left(0,\frac{8}{9}\right) [/tex]


Daniel.
 

Related to A weird domain and range? anybody up for a challenge

1. What is a weird domain and range?

A weird domain and range refers to a set of input and output values that are unconventional or unexpected. This can occur in mathematical functions, scientific experiments, or any other situation where a relationship between two variables is being explored.

2. How do you determine if a domain and range is weird?

A domain and range can be considered weird if the values do not follow a predictable pattern or if there are outliers that significantly affect the relationship between the variables. This can be determined through data analysis and statistical methods.

3. What causes a weird domain and range?

A weird domain and range can be caused by various factors, such as errors in data collection, experimental design flaws, or the presence of unusual or unexpected variables that affect the relationship between the input and output values.

4. Can a weird domain and range be useful?

Yes, a weird domain and range can be useful in certain situations. It can lead to the discovery of new relationships or variables that were previously unknown, and can also challenge existing theories and assumptions.

5. How can a weird domain and range impact scientific research?

A weird domain and range can have a significant impact on scientific research as it can lead to unexpected results and conclusions. It may also require researchers to reevaluate their methods and theories in order to better understand the relationship between variables.

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