Calc 3 Range of a function (set of points)

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Homework Help Overview

The discussion revolves around understanding the range of a function in the context of a calculus problem, specifically focusing on inequalities and transformations applied to them. Participants are examining the steps taken in a solution involving the manipulation of inequalities and the implications of multiplying by negative numbers.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants express confusion about the transition between steps in the solution, particularly regarding the origin of certain constants and the effects of multiplying inequalities by negative numbers. Questions arise about the treatment of inequality signs during these transformations.

Discussion Status

The discussion is active, with participants seeking clarification on specific steps and reasoning. Some have provided insights into the manipulation of inequalities, and there appears to be a growing understanding among participants as they engage with each other's questions and responses.

Contextual Notes

Participants are working from an image that contains the original problem statement and equations, which are not fully detailed in the text. There is a noted concern about the handling of inequalities when multiplied by negative numbers, reflecting a common area of confusion in mathematical reasoning.

xtrubambinoxpr
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Homework Statement



See attached image

Homework Equations



they are provided in the image. I see the domain is used

The Attempt at a Solution



I can't figure out how they went from step one to step 2. where does the -81 come from and the 9 multiplied to the function in the middle. I tried to figure it out and all i got was divide everything by 9 then multiplying by 18 across to get 9 in the middle but that won't get me 81 on the eft hand side.

Thank you in advance!
 

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xtrubambinoxpr said:

Homework Statement



See attached image

Homework Equations



they are provided in the image. I see the domain is used

The Attempt at a Solution



I can't figure out how they went from step one to step 2. where does the -81 come from and the 9 multiplied to the function in the middle. I tried to figure it out and all i got was divide everything by 9 then multiplying by 18 across to get 9 in the middle but that won't get me 81 on the eft hand side.

Thank you in advance!

What happens to the first batch of inequalities when you multiply everything by -9?
 
gopher_p said:
What happens to the first batch of inequalities when you multiply everything by -9?
Well I'm pretty retarded lol
But what about the greater than or equal to signs? And why weren't they reversed? Like from elementary you learn to flip them if it's anything with a negative number.
 
xtrubambinoxpr said:
Well I'm pretty retarded lol

I doubt that very much if you're taking Calc 3. Inexperienced? Almost definitely. Ill prepared? Possibly. Too stupid? Not very likely.

But what about the greater than or equal to signs? And why weren't they reversed? Like from elementary you learn to flip them if it's anything with a negative number.

Look again. The inequalities were flipped, and then the whole line was flipped.
 
gopher_p said:
I doubt that very much if you're taking Calc 3. Inexperienced? Almost definitely. Ill prepared? Possibly. Too stupid? Not very likely.

Look again. The inequalities were flipped, and then the whole line was flipped.
Ahhhhh I see it now! Thanks a lot! This helps a lot this section because I couldn't put the pieces together!
 

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