Range and domain of y = 24 - 2x with positive constraints

[okunyg]

I'm sorry for this, but what is the range and domain of the following function?

y = 24 - 2x

y has to be positive (y > 0) and x too (x > 0)

How would you solve this? Do you just need a look and then be able to write it down? Or do you need to solve it with algebra?

I've found that x can only be up to 12, or else y would be negative:

y = 24 - 2x
0 = 24 - 2x
x = 12

What is then the minimum of x?

2x = 24 - y
0 = 24 - y
y = 24

When y is 24, x is zero.

This means:
0 < x < 12

With these values, y is always positive, we have solved the domain of the function.

Is this correct?

 

[neutrino]

This means:
0 < x < 12

With these values, y is always positive, we have solved the domain of the function.

Is this correct?

That's right.

 

[morson]

y > 0 implies 24 - 2x > 0 implies x < 12

x > 0 implies 12 - 0.5y > 0 implies y < 24

So: 0 < x < 12

And: 0 < y < 24

Good work. Also, don't apologise for wanting help.

 

[okunyg]

Thanks.


But apparently the correct answer is:

6 < x < 12 and
0 < y < 12

Is the key (answer) in the back of the book misprinted perhaps?

 

[ice109]

Thanks.


But apparently the correct answer is:

6 < x < 12 and
0 < y < 12

Is the key (answer) in the back of the book misprinted perhaps?

yes completely wrong