with these equation (fog)oh and fo(goh) solve this problem 
f ( x ) = 2 x
g(X) = 3x-1
h(x) = x square + 3 

To solve the problem involving the composite functions \((f \circ g) \circ h\) and \(f \circ (g \circ h)\), we need to evaluate each composite function step by step using the given functions:

Given:
- \( f(x) = 2x \)
- \( g(x) = 3x - 1 \)
- \( h(x) = x^2 + 3 \)

### 1. \((f \circ g) \circ h\)
This means we first need to find \(f \circ g(x)\), and then apply this result to \(h(x)\).

#### Step 1: Find \(f \circ g(x)\)
\[
f(g(x)) = f(3x - 1)
\]
Substitute \(g(x) = 3x - 1\) into \(f(x)\):
\[
f(3x - 1) = 2(3x - 1) = 6x - 2
\]

#### Step 2: Apply \(h(x)\) to the result
Now, we need to substitute \(h(x)\) into the result from Step 1:
\[
(f \circ g)(h(x)) = (6h(x) - 2)
\]
Since \(h(x) = x^2 + 3\):
\[
(f \circ g)(h(x)) = 6(x^2 + 3) - 2 = 6x^2 + 18 - 2 = 6x^2 + 16
\]
Thus,
\[
(f \circ g) \circ h(x) = 6x^2 + 16
\]

### 2. \(f \circ (g \circ h)\)
This means we first need to find \(g \circ h(x)\), and then apply this result to \(f(x)\).

#### Step 1: Find \(g \circ h(x)\)
\[
g(h(x)) = g(x^2 + 3)
\]
Substitute \(h(x) = x^2 + 3\) into \(g(x)\):
\[
g(x^2 + 3) = 3(x^2 + 3) - 1 = 3x^2 + 9 - 1 = 3x^2 + 8
\]

#### Step 2: Apply \(f(x)\) to the result
Now, we need to substitute \(g(h(x))\) into \(f(x)\):
\[
f(g(h(x))) = f(3x^2 + 8)
\]
Substitute into \(f(x)\):
\[
f(3x^2 + 8) = 2(3x^2 + 8) = 6x^2 + 16
\]
Thus,
\[
f \circ (g \circ h)(x) = 6x^2 + 16
\]

### Conclusion
For both \((f \circ g) \circ h(x)\) and \(f \circ (g \circ h)(x)\), the result is the same:
\[
\boxed{6x^2 + 16}
\]

Would you like to go over the details of these steps or ask any further questions?

### Related Questions:
1. How do you find the composition of more complex functions?
2. What happens if the functions have different domains?
3. How would the process change if one of the functions were non-linear?
4. Can you verify that composite functions are associative in this case?
5. How can you apply these operations to functions involving trigonometric or logarithmic expressions?

**Tip:** When working with composite functions, always solve from the inside out, dealing with each function step by step to avoid errors.

Explore how to solve composite functions involving quadratic equations with detailed steps and examples. This problem covers composite functions, function composition, and quadratic equations, suitable for advanced high school students.

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