If (f o g)= 16x + 7 and g(x)= 2x - 1 , find f(x)

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Homework Help Overview

The problem involves finding the function f(x) given the composition of functions (f o g) = 16x + 7 and g(x) = 2x - 1. The context is within the subject area of function composition and linear functions.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the method of substituting g(x) into (f o g) to derive f(x). There is uncertainty about the correctness of the initial attempts and whether the resulting expressions are accurate. Some participants suggest verifying by plugging g(x) back into f(g(x)).

Discussion Status

The discussion is ongoing with participants exploring different interpretations of the problem. Some guidance has been offered regarding the structure of f(x) as a linear function, and there is a suggestion to consider the composition involving the inverse of g.

Contextual Notes

There is a note that the problem may be better suited for a different subforum, indicating potential confusion about the appropriate level of discussion for the topic.

Andolph23
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Homework Statement



If (f o g)= 16x + 7 and g(x)= 2x - 1 , find f(x)


The Attempt at a Solution



I haven't done a problem like this in awhile so I don't remember exactly what to do. I think you plug g(x) into (f o g) to get 32x - 9 but I'm not sure if that's correct.

Homework Statement

 
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Andolph23 said:

Homework Statement



If (f o g)= 16x + 7 and g(x)= 2x - 1 , find f(x)


The Attempt at a Solution



I haven't done a problem like this in awhile so I don't remember exactly what to do. I think you plug g(x) into (f o g) to get 32x - 9 but I'm not sure if that's correct.

Homework Statement


If this is correct, you should try f(g(x)) and see if you get what it was originally

P.S. Notice your trying to get f(x)
 
Suppose that f(x) = Ax + B, a linear function. Given that, and that g(x) = 2x - 1, what is (f o g)(x)?
(Ignore for a moment that (f o g)(x) was already given.)

P.S. This should really be in the Precalculus subforum.
 
What is (f○g○g-1)(x) ?
 
SammyS said:
What is (f○g○g-1)(x) ?

Wow, your good:wink: Didn't even think of that.
 

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