Calc 3 Range of a function (set of points)

[xtrubambinoxpr]

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!

 

[gopher_p]

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?

 

[xtrubambinoxpr]

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.

 

[gopher_p]

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.

 

[xtrubambinoxpr]

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!