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

• Jaco Viljoen
In summary, the domain of a function refers to the set of all possible input values and is typically represented using interval or set notation. It can be undefined if there are restrictions on the input values, and can be determined by considering the type of function and any potential restrictions. It is important to know the domain of a function to ensure it is well-defined and to identify any potential issues or restrictions.
Jaco Viljoen

## Homework Statement

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

g(x)=-(1/2)x-3
l(x)=√(2-x)-3

## The Attempt at a Solution

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

The problem asked for the domain of l/g.

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

Jaco Viljoen
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.

Jaco Viljoen
Jaco Viljoen said:

## Homework Statement

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

g(x)=-(1/2)x-3
l(x)=√(2-x)-3

## The Attempt at a Solution

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

Jaco Viljoen said:
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.

Jaco Viljoen said:
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.

Jaco Viljoen said:

## Homework Statement

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

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

Thank you for the help.
Jaco

Jaco Viljoen said:
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 Dl/g but then went on to find Dg/l.

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

Jaco Viljoen

## 1) What does the term "domain" mean in this context?

The domain of a function refers to the set of all possible input values for that function. In other words, it is the set of numbers that can be plugged into the function to produce a valid output.

## 2) How is the domain of a function typically represented?

The domain of a function is typically represented using interval notation or set notation. For example, if the function is defined over all real numbers, the domain would be represented as (-∞, ∞). If the function is only defined for positive numbers, the domain would be represented as (0, ∞).

## 3) Can the domain of a function ever be undefined?

Yes, the domain of a function can be undefined if there are certain restrictions placed on the input values. For example, if the function contains a term that cannot be divided by zero, the domain would be undefined for any input that would make that term equal to zero.

## 4) How can you determine the domain of a function without calculating the function itself?

The domain of a function can be determined by looking for any restrictions on the input values, such as division by zero or taking the square root of a negative number. Additionally, the domain can also be determined by considering the type of function and the set of numbers it is typically defined over.

## 5) Why is it important to know the domain of a function?

Knowing the domain of a function is important because it helps to ensure that the function is well-defined and that any calculations or manipulations involving the function are valid. It also helps to identify any potential issues or restrictions with the function and allows for a better understanding of its behavior.

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