Math help ASAP

Nov 2018
1
0
Virginia
I have been having trouble with htis problem for a while, nad my teacher won't give me any feedback on the problem. This is a huge part of my grade so it is important, and I wondering if I could receive help? Here is the problem:

Imagine that you live on an infinitely long and straight street called Infinite Drive. The addresses on Infinite Drive are given by real numbers. Your address on the street is 𝜋 while your friend Patrick’s is √3 and Karen’s is sin60°. There are two moving companies, 𝑓 and 𝑔. Those companies move people along Infinite Drive from address 𝑥 to new addresses 𝑓(𝑥) or 𝑔(𝑥), depending on which company people choose. Assume that the functions 𝑓(𝑥) = 1 − 𝑥 and 𝑔(𝑥) = 1 𝑥 describe how the moving companies move people from one address to another. a. Find 𝑓(𝑔(𝑥)) and 𝑔(𝑓(𝑥)). b. Evaluate your answers from a for 𝑥 = 𝜋, your address. c. Evaluate your answers from a for 𝑥 = 0, your parents’ address. Explain the significance of this answer. 2. Now assume that the moving companies are described by the functions 𝑓(𝑥) = 5𝑥 and 𝑔(𝑥) = 1 𝑥 . a. Find 𝑓(𝑔(𝑥)) and 𝑔(𝑓(𝑥)). b. Evaluate your answers from a for 𝑥 = 𝜋, your address. 3. Notice that the functions in Part 1 have the property that 𝑓 = 𝑓−1 and 𝑔 = 𝑔−1. That is, the inverse of 𝑓 is equal to itself and the inverse of 𝑔 is also equal to itself. Take the composition of each function with itself to show that this is true. Remember, if the function ℎ(𝑥) is equal to its own inverse, then ℎ ∘ ℎ−1 = 𝑥.
 

romsek

Math Team
Sep 2015
2,958
1,673
USA
I don't think your specification for $g(x)$ came through correctly.

It would help if you split things into paragraphs as well.
 

SDK

Sep 2016
797
541
USA
I have been having trouble with htis problem for a while, nad my teacher won't give me any feedback on the problem. This is a huge part of my grade so it is important, and I wondering if I could receive help? Here is the problem:

Imagine that you live on an infinitely long and straight street called Infinite Drive. The addresses on Infinite Drive are given by real numbers. Your address on the street is 𝜋 while your friend Patrick’s is √3 and Karen’s is sin60°. There are two moving companies, 𝑓 and 𝑔. Those companies move people along Infinite Drive from address 𝑥 to new addresses 𝑓(𝑥) or 𝑔(𝑥), depending on which company people choose. Assume that the functions 𝑓(𝑥) = 1 − 𝑥 and 𝑔(𝑥) = 1 𝑥 describe how the moving companies move people from one address to another. a. Find 𝑓(𝑔(𝑥)) and 𝑔(𝑓(𝑥)). b. Evaluate your answers from a for 𝑥 = 𝜋, your address. c. Evaluate your answers from a for 𝑥 = 0, your parents’ address. Explain the significance of this answer. 2. Now assume that the moving companies are described by the functions 𝑓(𝑥) = 5𝑥 and 𝑔(𝑥) = 1 𝑥 . a. Find 𝑓(𝑔(𝑥)) and 𝑔(𝑓(𝑥)). b. Evaluate your answers from a for 𝑥 = 𝜋, your address. 3. Notice that the functions in Part 1 have the property that 𝑓 = 𝑓−1 and 𝑔 = 𝑔−1. That is, the inverse of 𝑓 is equal to itself and the inverse of 𝑔 is also equal to itself. Take the composition of each function with itself to show that this is true. Remember, if the function ℎ(𝑥) is equal to its own inverse, then ℎ ∘ ℎ−1 = 𝑥.
In my head this translated to:

This problem requires me to spend some time thinking about things and I'm unwilling to do that. My teacher wouldn't give me the answer so I hope someone here will.

Is that about right?
 
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Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
Your address on the street is 𝜋
while your friend Patrick’s is √3
and Karen’s is sin60°.
[....Karen(-.3048)..<|>...Pat(1.7321).....Me(3.1416).........]:Silva street

I wanna Karen to move in with me...