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

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The discussion focuses on finding the composition of functions for given pairs, specifically asking for detailed working on examples. Participants are encouraged to clarify which compositions they are attempting to find, such as (f∘g)(x). There is a noted absence of definitions for part b), which hinders progress. The community emphasizes the importance of sharing attempted solutions to facilitate guidance and learning. Active engagement in problem-solving is a key goal of the discussion.
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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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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
 
Some of these problems have been considered in https://driven2services.com/staging/mh/index.php?threads/13132/.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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