find f ∘ f in f(x)= square root of x, g(x)= x^2-1

To find \( f \circ f(x) \) where \( f(x) = \sqrt{x} \) and \( g(x) = x^2 - 1 \), you need to substitute the function \( f(x) \) into itself.

### Step-by-Step Solution:

1. **Identify the function**:
   - \( f(x) = \sqrt{x} \)

2. **Substitute \( f(x) \) into itself**:
   - \( f(f(x)) = f(\sqrt{x}) \)

3. **Apply the function \( f(x) \) again**:
   - Since \( f(x) = \sqrt{x} \), substitute \( \sqrt{x} \) into \( f(x) \):
   - \( f(f(x)) = \sqrt{\sqrt{x}} \)

4. **Simplify**:
   - \( f(f(x)) = \sqrt{x^{1/2}} = x^{1/4} \)

So, \( f \circ f(x) = x^{1/4} \).

The function \( g(x) = x^2 - 1 \) is not needed in this computation since you only asked for \( f \circ f(x) \).

Would you like more details on this process or have any further questions?

### Related Questions:
1. What is \( f(g(x)) \) when \( g(x) = x^2 - 1 \) and \( f(x) = \sqrt{x} \)?
2. How do you find \( g \circ g(x) \) when \( g(x) = x^2 - 1 \)?
3. What is the domain of \( f \circ f(x) = x^{1/4} \)?
4. How would you graph \( f \circ f(x) \)?
5. What is the inverse of \( f \circ f(x) \) when \( f(x) = \sqrt{x} \)?

### Tip:
When composing a function with itself, make sure to correctly apply the function's operations at each step, and simplify the result properly.

Learn how to find f ∘ f for the functions f(x) = square root of x and g(x) = x^2 - 1. Follow a detailed step-by-step solution to compute f ∘ f(x) and understand the composition of functions. Suitable for advanced high school students and anyone interested in function composition.

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