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The image shows a problem involving composite functions. Here is the text extracted from the image:

Given:
\[
f(x) = x^2 - 1, \quad g(x) = x - 1, \quad h(x) = \sqrt{x}
\]

Find: \(f(g(h(x)))\)

### Solution:

To find \(f(g(h(x)))\), we will evaluate the functions step-by-step from the inside out.

1. **Find \(h(x)\):**
   \[
   h(x) = \sqrt{x}
   \]

2. **Evaluate \(g(h(x))\):**
   Substitute \(h(x)\) into \(g(x)\):
   \[
   g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 1
   \]

3. **Evaluate \(f(g(h(x)))\):**
   Substitute \(g(h(x))\) into \(f(x)\):
   \[
   f(g(h(x))) = f(\sqrt{x} - 1)
   \]
   Now, substitute \(\sqrt{x} - 1\) into \(f(x)\):
   \[
   f(\sqrt{x} - 1) = (\sqrt{x} - 1)^2 - 1
   \]

4. **Simplify the expression:**
   \[
   (\sqrt{x} - 1)^2 - 1 = (\sqrt{x})^2 - 2\sqrt{x} + 1 - 1 = x - 2\sqrt{x}
   \]

### Final Answer:
\[
f(g(h(x))) = x - 2\sqrt{x}
\]

Would you like more details on this solution, or do you have any questions?

### Related Questions:
1. What is the domain of the function \(f(g(h(x)))\)?
2. How would you find \(g(f(x))\) given the same functions?
3. What would \(h(f(g(x)))\) look like?
4. How do you find the inverse of a composite function like \(f(g(x))\)?
5. How does the composition of functions affect their domains?

### Tip:
When dealing with composite functions, always work from the inside out to ensure you substitute and simplify correctly.

Find f(g(h(x))) given f(x) = x^2 - 1, g(x) = x - 1, h(x) = sqrt(x).

Learn how to solve a composite function f(g(h(x))) where f(x) = x^2 - 1, g(x) = x - 1, and h(x) = sqrt(x). This problem involves function composition, quadratic expressions, and square roots, with a step-by-step solution.

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