Correct use of parentheses is important .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
Homework Equations
none
The Attempt at a Solution
f(x) = x/(x-3)
g(x) 3/(x-3)
?
Therefore, your choices for f(x) and g(x) look good !Torshi said:Lim x->3+ (x-3)/(x-3) = 1? ≠0
SammyS said:Therefore, your choices for f(x) and g(x) look good !
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.
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.
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.
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.
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.