Composite Functions: f o g (x) = Abs(x), f(x) = root(x), g(x) = Abs(x)

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Homework Help Overview

The discussion revolves around composite functions, specifically analyzing the relationship between functions f and g, where f o g (x) is stated to equal Abs(x). The subject area includes function composition and properties of absolute values and square roots.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are exploring the definitions of f(x) and g(x) and questioning whether the original problem statement is accurate. There is a suggestion that if f o g (x) equals Abs(x), then the roles of f and g might need reconsideration.

Discussion Status

The discussion is active, with participants offering different interpretations of the functions involved. Some guidance has been provided regarding potential definitions of f and g, but no consensus has been reached on the correct setup.

Contextual Notes

One participant insists that the problem is correctly stated as taken from a textbook, which raises questions about the assumptions being made regarding the functions' definitions and their domains.

Larrytsai
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f o g (x) = Abs(x)
f(x)=?
g(x)= root(x)

im thinking f(x) is = to root(x) correct me if I am wrong?
 
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f(x) = sqrt(x) doesn't work. Are you sure you have this problem written correctly? Could it be g o f (x) = Abs(x)? That would make more sense with g(x) being sqrt(x). Of if it is indeed f o g (x) = Abs(x), could it be that f(x) = sqrt(x) and you need to find g(x)?
 
its correct way i took it straight from the book.
 
OK.
If f(x) = x2 and g(x) = [tex]\sqrt{x}[/tex]
then [itex](f~\circ~g )(x) = x[/itex].

Since the domain of g = {x | x [itex]\geq[/itex] 0}, then x = |x| in this case.
 

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