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Question 537893: If f(x)=4x-5 find f(3a+1) please help and demostrate details please.and explain to me whats function is. (im in 8th grade and learning algebra.)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First some terminology:  is a typical way of representing a function. A function is a mathematical relationship between one or more independent variables (the input) and a dependent variable (the output). For now, we will only consider functions that have a single input or independent variable. A function must have the property that for any given independent variable, you can only have a single dependent variable value.
Think of a mathematical relationship like a box. On the front end of the box is a slot, like a coin slot on a gumball machine, and on the other end is a tray, like where you get the gumball once you have turned the knob on the machine. And speaking of the knob or crank, that is on the side of the box. You take an input value, or independent variable value, or x and insert it into the slot in the front. Then you turn the crank and an independent variable value () ) lands in the tray on the other end.
Now if the machinery inside the box allows different values of ) to be generated when some particular value of  is put into the slot, for example if you put  in the slot and sometimes you get  out in the tray but sometimes you get  instead, then this particular machine IS NOT a function, it is simply a relation.
Note that it is perfectly ok for the machine to give you the same value for different values of the input, for example if I put in the number  and get  as an output and then put in the number  and also get out, then we still have a function.
As I mentioned earlier, is a typical way to represent a function. This needs to be differentiated from which specifically means "the value of the function at "
In most cases when you see something like \ =\ 4x\ -\ 5) , this is just a definition of the inner workings of one particular machine that has a slot, a tray, and a crank.
Your problem is asking you to describe what happens when, instead of being submitted to the machine, you submit  . The answer, in general, is that whatever was supposed to happen to must now happen to . The process is quite simple: Take the definition of your function:
\ =\ 4x\ -\ 5)
And every place you see an , replace it with , thus:
\ =\ 4(3a\ +\ 1)\ -\ 5)
The only thing left to do is to use the distributive property and collect like terms in the RHS to simplify.
Super-deluxe Double-plus Extra Credit
Write the meaning of ) in an English sentence.
John
My calculator said it, I believe it, that settles it
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