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November 15th, 2018, 05:41 AM   #1
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Math help ASAP

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œ‹ while your friend Patrick’s is √3 and Karen’s is sin60Β°. There are two moving companies, 𝑓 and 𝑔. Those companies move people along Infinite Drive from address π‘₯ to new addresses 𝑓(π‘₯) or 𝑔(π‘₯), depending on which company people choose. Assume that the functions 𝑓(π‘₯) = 1 βˆ’ π‘₯ and 𝑔(π‘₯) = 1 π‘₯ describe how the moving companies move people from one address to another. a. Find 𝑓(𝑔(π‘₯)) and 𝑔(𝑓(π‘₯)). b. Evaluate your answers from a for π‘₯ = πœ‹, your address. c. Evaluate your answers from a for π‘₯ = 0, your parents’ address. Explain the significance of this answer. 2. Now assume that the moving companies are described by the functions 𝑓(π‘₯) = 5π‘₯ and 𝑔(π‘₯) = 1 π‘₯ . a. Find 𝑓(𝑔(π‘₯)) and 𝑔(𝑓(π‘₯)). b. Evaluate your answers from a for π‘₯ = πœ‹, your address. 3. Notice that the functions in Part 1 have the property that 𝑓 = π‘“βˆ’1 and 𝑔 = π‘”βˆ’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 β„Ž(π‘₯) is equal to its own inverse, then β„Ž ∘ β„Žβˆ’1 = π‘₯.
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November 16th, 2018, 12:41 AM   #2
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I don't think your specification for $g(x)$ came through correctly.

It would help if you split things into paragraphs as well.
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November 16th, 2018, 07:14 AM   #3
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Quote:
Originally Posted by Silva View Post
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œ‹ while your friend Patrick’s is √3 and Karen’s is sin60Β°. There are two moving companies, 𝑓 and 𝑔. Those companies move people along Infinite Drive from address π‘₯ to new addresses 𝑓(π‘₯) or 𝑔(π‘₯), depending on which company people choose. Assume that the functions 𝑓(π‘₯) = 1 βˆ’ π‘₯ and 𝑔(π‘₯) = 1 π‘₯ describe how the moving companies move people from one address to another. a. Find 𝑓(𝑔(π‘₯)) and 𝑔(𝑓(π‘₯)). b. Evaluate your answers from a for π‘₯ = πœ‹, your address. c. Evaluate your answers from a for π‘₯ = 0, your parents’ address. Explain the significance of this answer. 2. Now assume that the moving companies are described by the functions 𝑓(π‘₯) = 5π‘₯ and 𝑔(π‘₯) = 1 π‘₯ . a. Find 𝑓(𝑔(π‘₯)) and 𝑔(𝑓(π‘₯)). b. Evaluate your answers from a for π‘₯ = πœ‹, your address. 3. Notice that the functions in Part 1 have the property that 𝑓 = π‘“βˆ’1 and 𝑔 = π‘”βˆ’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 β„Ž(π‘₯) is equal to its own inverse, then β„Ž ∘ β„Žβˆ’1 = π‘₯.
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?
Thanks from topsquark
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November 16th, 2018, 08:11 AM   #4
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Quote:
Originally Posted by Silva View Post
Your address on the street is πœ‹
while your friend Patrick’s is √3
and Karen’s is sin60Β°.
[....Karen(-.3048)..<|>...Pat(1.7321).....Me(3.1416).........]:Silva street

I wanna Karen to move in with me...
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