if f(x) = √(x-3) , g(x) = √(x^2+3)

what is the composition of (f o g)

The composition of functions \((f \circ g)(x)\) means applying \(g(x)\) first and then applying \(f(x)\) to the result. In this case:

1. \(g(x) = \sqrt{x^2 + 3}\)
2. Now, apply \(f(x)\) to the result of \(g(x)\):  
   \(f(g(x)) = f\left(\sqrt{x^2 + 3}\right)\)

Since \(f(x) = \sqrt{x - 3}\), we substitute \(\sqrt{x^2 + 3}\) into \(f(x)\):

\[
(f \circ g)(x) = \sqrt{\left(\sqrt{x^2 + 3}\right) - 3}
\]

Simplifying the expression inside the square root:

\[
(f \circ g)(x) = \sqrt{x^2 + 3 - 3} = \sqrt{x^2}
\]

\[
(f \circ g)(x) = |x|
\]

Thus, the composition of \(f\) and \(g\) is \((f \circ g)(x) = |x|\).

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you find the domain of a composed function?
2. What is the domain of \(f(x) = \sqrt{x-3}\)?
3. What is the domain of \(g(x) = \sqrt{x^2 + 3}\)?
4. How would you compute \((g \circ f)(x)\)?
5. How does the absolute value appear in the final result?

**Tip:** When working with square root functions, always check the domain to ensure you’re not taking the square root of a negative number.

if f(x) = √(x-3) , g(x) = √(x^2+3) what is the composition of (f o g)

Learn how to find the composition of functions f(x) = √(x - 3) and g(x) = √(x^2 + 3). This problem covers function composition and simplification, resulting in (f ∘ g)(x) = |x|. Suitable for students in Grades 9-12.

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