To find $(f \circ g)(x)$, also written as $f(g(x))$, we substitute $g(x) = -6x + 1$ into $f(x)$.

Given:

• $f(x) = 6x - 5$
• $g(x) = -6x + 1$

Step-by-step solution:

1. Replace $x$ in $f(x)$ with $g(x)$: $f(g(x)) = 6(-6x + 1) - 5$

2. Simplify: $f(g(x)) = 6(-6x) + 6(1) - 5$ $f(g(x)) = -36x + 6 - 5$

3. Combine like terms: $f(g(x)) = -36x + 1$

Final Answer:

$(f \circ g)(x) = -36x + 1$

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Would you like further clarification or an alternative explanation?

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Related Questions:

1. How do you find $(g \circ f)(x)$ for the same functions?
2. What happens if $f(x)$ and $g(x)$ are swapped in composition?
3. Can the result $(f \circ g)(x)$ be visualized graphically?
4. What is the domain of $(f \circ g)(x)$ given these functions?
5. How does composition of functions relate to inverse functions?

Tip:

Always check for domain restrictions when composing functions, especially if square roots or fractions are involved.