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

In summary, f o g (x) = Abs(x) is a function composition where f(x) is equal to the absolute value of x and g(x) is equal to the square root of x. This means that the result of the composition is x, and since the domain of g is limited to non-negative values, x is equivalent to |x|.
  • #1
Larrytsai
228
0
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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  • #2
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)?
 
  • #3
its correct way i took it straight from the book.
 
  • #4
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.
 

1. What is a composite function?

A composite function is a function that is formed by combining two or more functions. In this case, f o g (x) is formed by combining the functions f(x) and g(x).

2. How do you read and interpret the notation f o g (x)?

The notation f o g (x) is read as "f of g of x" or "f composed with g of x". This means that the output of g(x) is used as the input for f(x).

3. What is the order of operations when evaluating a composite function?

The order of operations for evaluating a composite function is to first evaluate the innermost function, in this case g(x), and then use the output as the input for the outer function, f(x).

4. What are the domain and range of the composite function f o g (x) in this example?

The domain of f o g (x) is all real numbers because the absolute value function and square root function are defined for all real numbers. The range is limited to non-negative real numbers because the output of g(x) is always positive or zero, and the output of f(x) is the square root of the input, which cannot be negative.

5. How would you graph the composite function f o g (x) in this example?

To graph the composite function f o g (x), first graph g(x) and then apply the transformation of f(x) on the graph of g(x). In this case, the graph of f(x) would be a reflection of the graph of g(x) over the y-axis, followed by a shift to the right by 1 unit.

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