- #1
Deagonx
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Homework Statement
g(f(x))
g(x) = 3/x+1
f(x)= 3x+2
Homework Equations
?
The Attempt at a Solution
Ive had none I don't even know how to attempt this problem.
Deagonx said:Homework Statement
g(f(x))
g(x) = 3/x+1
f(x)= 3x+2
Homework Equations
?
The Attempt at a Solution
Ive had none I don't even know how to attempt this problem.
Deagonx said:They way that I did it was as followed:
If f(x) = 3x + 2. and the equation is g(f(x)) then isn't it really just g(3x+2)
In which case, I came to 3/(3x+2) + 1 which I then simplified to x + 2.5 Which I think is wrong.
dynamicsolo said:This part is correct.
So [tex] f( g(x) ) = \frac{3}{(3x+2) + 1 } = \frac{3}{3x + 3} .[/tex] What would that simplify to?
Deagonx said:They way that I did it was as followed:
If f(x) = 3x + 2. and the equation is g(f(x)) then isn't it really just g(3x+2)
In which case, I came to 3/(3x+2) + 1 which I then simplified to x + 2.5 Which I think is wrong.
dynamicsolo said:Evidently, everyone still hasn't settled on what g(x) is ...
The purpose of solving G(f(x)) is to find the value of the composition function when given a specific input value for x. This helps to simplify complex functions and make them easier to understand and work with.
To solve G(f(x)), you must first substitute the given value for x into the inner function, f(x). Then, take the result and substitute it into the outer function, G(x). Finally, simplify the expression to find the value of G(f(x)).
G(f(x)) is a composition function, meaning it is the result of applying one function (f(x)) to another function (G(x)). f(x) is a standalone function that may or may not be used in a composition function.
Yes, you can solve G(f(x)) for multiple values of x. Simply substitute each value into the inner function, f(x), and then substitute the result into the outer function, G(x), to find the corresponding value of G(f(x)).
Solving G(f(x)) can be applied in real-world scenarios such as finance, physics, and engineering. It can help to model and analyze complex systems by breaking them down into simpler functions. It is also useful in predicting and understanding patterns and relationships in data.