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.