To find $(f \circ g)(x)$, we substitute $g(x)$ into $f(x)$:

Given functions:

• $f(x) = x^2 + 12$
• $g(x) = \sqrt{3x + 2}$

Compute $(f \circ g)(x)$:

$(f \circ g)(x) = f(g(x)) = f(\sqrt{3x + 2})$ Since $f(x) = x^2 + 12$, replacing $x$ with $g(x)$:

$f(g(x)) = (\sqrt{3x + 2})^2 + 12$

$= (3x + 2) + 12$

$= 3x + 14$

Final Answer:

$(f \circ g)(x) = 3x + 14$

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Related Questions:

1. How do you find $(g \circ f)(x)$?
2. What is the domain of $(f \circ g)(x)$?
3. How do composition functions relate to inverse functions?
4. Can function composition be commutative?
5. How do you verify if a function composition is valid?

Tip:

Always check the domain restrictions when composing functions, as some inputs might be undefined in the inner function!