https://file.aiquickdraw.com/mathbot/file/1725960558864rtdycpb8.jpg

The image contains two given functions and asks to find the composition of these functions. Here's the information extracted:

Given equations:
1. \( f(x) = \sqrt{x - 1} \)
2. \( g(x) = x^2 - 3 \)

The problem asks for the composition \( (f \circ g)(x) \), which is read as "f composed with g of x."

### Step-by-Step Solution:

To find \( (f \circ g)(x) \), we substitute \( g(x) \) into \( f(x) \). That is:
\[
(f \circ g)(x) = f(g(x))
\]

We know:
- \( f(x) = \sqrt{x - 1} \)
- \( g(x) = x^2 - 3 \)

Thus, substituting \( g(x) \) into \( f(x) \):
\[
(f \circ g)(x) = \sqrt{(x^2 - 3) - 1} = \sqrt{x^2 - 4}
\]

### Final Answer:
\[
(f \circ g)(x) = \sqrt{x^2 - 4}
\]

Would you like further clarification or details on this solution? 

Here are some related questions for practice:
1. What is \( g \circ f(x) \), the reverse composition of the functions?
2. How do you find the domain of \( f(x) = \sqrt{x-1} \)?
3. What is the domain of \( (f \circ g)(x) \)?
4. How would you differentiate \( (f \circ g)(x) \)?
5. Can you find the inverse of \( f(x) = \sqrt{x-1} \)?

**Tip:** When solving function compositions, always substitute carefully and simplify the expressions step by step.

Diberikan persamaan: f(x) = √(x - 1) dan g(x) = x² - 3. Hitung (f ∘ g)(x).

Explore the step-by-step solution to find the composition of functions (f ∘ g)(x) with f(x) = √(x - 1) and g(x) = x² - 3. This problem covers key concepts in function composition, square root functions, and quadratic expressions. Suitable for students in Grades 10-12.

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