Composition of Functions help please

In summary, to find g(x), replace x in f(x) with g(x), set it equal to f(g(x)), and solve for g(x). This may be a tedious process, but it will give you the answer.
  • #1
Gshandle
2
0

Homework Statement



Find g(x) if f(x) = (3x-1)/(2x+5) and f(g(x)) = (x+9)/(12x-11)

Homework Equations


N/A, as far as I know

The Attempt at a Solution



I tried doing it as though g(x) = y and it turned out like this:
(3y-1)/(2y+5)=(x+9)/(12x-11)
I very quickly saw that that wouldn't work though, so I'm kind of lost. This is independent work in order for me to be able to go into pre-calc, so while I can ask a teacher it is difficult to find time, hence why I'm relying on you guys :) Help would be much appreciated!
 
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  • #2
Think about it like this: you have f(x), and you have f(x) in the specific case when x=g(x), what you are looking for is what does x have to be in f(x) to give f(g(x)).

So, what does x have to be exchanged with in (3x-1)/(2x+5) to give (x+9)/(12x-11)
 
  • #3
Well, I already got that part of the logic which is why I set g(x) equal to y, but it didn't work, so I don't understand how to get it to work.
 
  • #4
Maybe you can find [itex]f^{-1}(y)[/itex]??

That is, set

[tex]y=\frac{3x-1}{2x+5}[/tex]

and try to find x in function of y.
 
  • #5
Ok, I just went through the math and its a bit of a long haul. Should be fairly easy but its tedious.

What you want to do is take your f(x) function, replace x with g(x), set it equal to your f(g(x)) function and then solve for g(x).
 

What is a composition of functions?

A composition of functions is when the output of one function is used as the input for another function. This creates a new function that combines the rules of the two original functions.

How do you notate a composition of functions?

The notation for a composition of functions is f(g(x)), where g(x) is the inner function and f(x) is the outer function. This is read as "f of g of x."

What is the domain and range of a composition of functions?

The domain of a composition of functions is the set of values that can be input into the inner function, while the range is the set of values that can be output from the outer function.

How do you evaluate a composition of functions?

To evaluate a composition of functions, you first evaluate the inner function using the given input. Then, take that output and use it as the input for the outer function. The result will be the final output of the composition of functions.

What are some real-life applications of composition of functions?

Composition of functions is commonly used in physics and engineering to model complex systems. It is also used in economics and finance to analyze the relationships between different variables. Additionally, it can be used in computer programming to create more efficient and flexible code.

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