What is the Domain of l/g Without first calculating (l/g)(x)

[Jaco Viljoen]

Homework Statement

Write down D_l/g without first calculating (l/g)(x)

Homework Equations

g(x)=-(1/2)x-3
l(x)=√(2-x)-3

The Attempt at a Solution

g(x)=-(1/2)x-3 D_g = {x∈ℝ}
l(x)=√(2-x)-3 D_l = {x∈ℝ:x≤2}
D_g/l = {x∈ℝ:x≤2}

 

[Fredrik]

The problem asked for the domain of l/g.

Why would the domain of g/l be the same as the domain of l?

 

[Mentallic]

As you guessed, you needed to find the intersection of both domains, but you're also forgetting one thing - there's a problem with division.

 

[SammyS]

Homework Statement

Write down D_l/g without first calculating (l/g)(x)

Homework Equations

g(x)=-(1/2)x-3
l(x)=√(2-x)-3

The Attempt at a Solution

g(x)=-(1/2)x-3 D_g = {x∈ℝ}
l(x)=√(2-x)-3 D_l = {x∈ℝ:x≤2}
D_g/l = {x∈ℝ:x≤2}

Not quite.

What does your textbook or notes say about the domain of the quotient of two functions?

 

[Jaco Viljoen]

Denominator can't be 0

g(x)=-(1/2)x-3 Dg = {x∈ℝ}
l(x)=√(2-x)-3 Dl = {x∈ℝ:x≤2}
l(x)≠0
Dg/l = {x∈ℝ:x≤2 and x≠-5}

 

[SammyS]

Denominator can't be 0

g(x)=-(1/2)x-3 Dg = {x∈ℝ}
l(x)=√(2-x)-3 Dl = {x∈ℝ:x≤2}
l(x)≠0
Dg/l = {x∈ℝ:x≤2 and x≠-5}

Looks good.

 

[Jaco Viljoen]

Thank you everyone.

 

[Mentallic]

Denominator can't be 0

g(x)=-(1/2)x-3 Dg = {x∈ℝ}
l(x)=√(2-x)-3 Dl = {x∈ℝ:x≤2}
l(x)≠0
Dg/l = {x∈ℝ:x≤2 and x≠-5}

Your thread title and opening sentence made it a little confusing, but you understand the process so that's all that matters.

Homework Statement

Write down D_l/g without first calculating (l/g)(x)

 

[Jaco Viljoen]

Thank you Mentallic,
what would a better title be for future use?

Thank you for the help.
Jaco

 

[Mentallic]

Thank you Mentallic,
what would a better title be for future use?

Thank you for the help.
Jaco

It wasn't so much the title as it was the confusion of the actual question. You mentioned calculating D_l/g but then went on to find D_g/l.

But regardless, a title such as "Domain of function" would suffice.