To find $(f \circ g)(x)$, we compute $f(g(x))$. This means substituting $g(x)$ into $f(x)$.

Given:

• $f(x) = 3x - 8$
• $g(x) = x - 6$

Step 1: Substitute $g(x) = x - 6$ into $f(x)$:

$f(g(x)) = f(x - 6)$

Step 2: Replace $x$ in $f(x)$ with $x - 6$:

$f(x - 6) = 3(x - 6) - 8$

Step 3: Simplify the expression:

$f(x - 6) = 3x - 18 - 8$ $f(x - 6) = 3x - 26$

Final Answer:

$(f \circ g)(x) = 3x - 26$

Let me know if you'd like further clarification or a step-by-step breakdown!

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Here are 5 related questions to practice:

1. What is $(g \circ f)(x)$ given the same $f(x)$ and $g(x)$?
2. If $h(x) = 2x + 4$, find $(f \circ h)(x)$.
3. Determine the domain of $(f \circ g)(x)$.
4. Verify if $(f \circ g)(x)$ is one-to-one.
5. If $g(x) = x^2 - 6x + 9$, find $(f \circ g)(x)$.

Tip: When composing functions, always substitute one function completely into the other before simplifying!