# Find a pair of functions such that the following are true

• Torshi
In summary, by finding a pair of functions f(x) and g(x) where their limit as x approaches 3 from the positive side is positive infinity, and the limit of their difference is not equal to 0, we can use f(x) = x/(x-3) and g(x) = 3/(x-3) as potential solutions. Correct use of parentheses is important as lim x→3+ (f(x)-g(x)) is not equal to 0 for these functions.
Torshi

## Homework Statement

Find a pair of functions f(x), g(x) such that the following are true

lim x->3+ f(x) = +∞
lim x->3+ g(x) = +∞
lim x->3+ (f(x)-g(x)) ≠0

none

f(x) = x/x-3
g(x) 3/x-3
?

Torshi said:

## Homework Statement

Find a pair of functions f(x), g(x) such that the following are true

lim x->3+ f(x) = +∞
lim x->3+ g(x) = +∞
lim x->3+ (f(x)-g(x)) ≠0

none

## The Attempt at a Solution

f(x) = x/(x-3)
g(x) 3/(x-3)
?
Correct use of parentheses is important .

Well, what is lim x→3+ (f(x)-g(x)) for those functions?

Lim x->3+ (x-3)/(x-3) = 1? ≠0

Torshi said:
Lim x->3+ (x-3)/(x-3) = 1? ≠0
Therefore, your choices for f(x) and g(x) look good !

SammyS said:
Therefore, your choices for f(x) and g(x) look good !

Thanks!

## 1. What is the definition of a pair of functions?

A pair of functions is a set of two related mathematical expressions or rules, where the input of one function is used as the input for the other function. This allows for the output of one function to be used as the input for the other function.

## 2. How can I find a pair of functions that satisfy certain conditions?

To find a pair of functions that satisfy certain conditions, you can start by identifying the conditions that need to be met. Then, you can use algebraic manipulation and/or graphing techniques to create two functions that meet those conditions. It may also be helpful to use known examples of functions, such as linear or quadratic functions, to guide your process.

## 3. Can a pair of functions have the same input but different outputs?

Yes, a pair of functions can have the same input but different outputs. This is because each function can have its own unique set of rules or expressions that determine the output for a given input. This is what allows for the output of one function to be used as the input for the other function.

## 4. Are there any limitations to finding a pair of functions?

There are some limitations to finding a pair of functions. These limitations can include the complexity of the conditions that need to be met, the availability of known examples of functions, and the ability to manipulate algebraic expressions or utilize graphing techniques. Additionally, some conditions may not have a solution that can be expressed in terms of functions.

## 5. How can I check if a pair of functions is correct?

To check if a pair of functions is correct, you can substitute different values for the input of one function and then use the resulting output as the input for the other function. If the output of the second function matches the original input of the first function, then the pair of functions is likely correct. Additionally, you can graph the two functions and see if they intersect at points that satisfy the given conditions.

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