How do you find the composition of functions in the given pairs?

In summary, we are asked to find the composition of two functions, f and g, defined for positive integers. The first pair of functions, f and g, are defined as f(n) = n + 60 and g(n) = 100n. The second pair, f and g, are not fully defined and require more information. The third pair, f and g, are defined as f(n) = log(n+3) and g(n) = log log(n+10). The last pair, f and g, are defined as f(n) = n log(n+2) and g(n).
  • #1
ash1
2
0
Please answer for this question with detailed working.

Let f and g be function from the positive integer defined by the following pairs f: N find the composition.

a) f(n) = n + 60 g (n) = 100n
b) f (n) = g(n) =
c) F(n) = log(n+3) g(n) = log log(n+10)
d) F(n) = n log (n+2) g(n)
 
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  • #2
What composition are you to find? ($(f\circ g)(x)$ for example?) Also, part b) is missing the function definitions.

Please post what you have tried so we know how best to help you. We do not just provide solutions; our goal is to help people work the problems themselves so that they are actively engaged in the process and learn. :D
 
  • #3
Some of these problems have been considered in https://driven2services.com/staging/mh/index.php?threads/13132/.
 

FAQ: How do you find the composition of functions in the given pairs?

What is function composition?

Function composition is a mathematical concept where two or more functions are combined to form a new function. This means that the output of one function becomes the input of another function.

What is the purpose of function composition?

The purpose of function composition is to create more complex and efficient functions by combining simpler functions. It can also help break down a complex problem into smaller, more manageable parts.

How is function composition represented?

Function composition is typically represented using the notation "f ∘ g" or "f(g(x))", where f and g are two functions and x is the input value.

What are the benefits of using function composition?

Function composition can help reduce code duplication and improve code organization. It also allows for more flexible and reusable code, as functions can be combined in different ways to achieve different results.

Are there any limitations to function composition?

One limitation of function composition is that it can only be performed on functions that have compatible inputs and outputs. Additionally, composing too many functions can make the code difficult to read and maintain.

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