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

Given Functions:

• $f(x) = 6x - 5$
• $g(x) = -6x + 1$

Substitution:

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

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

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

Final Answer:

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

Let me know if you'd like further details or have questions!
Here are 5 related questions to explore further:

1. What is $(g \circ f)(x)$ for the given functions?
2. How do you verify if $f(x)$ and $g(x)$ are inverses of each other?
3. Can you determine the domain and range of $(f \circ g)(x)$?
4. What happens when $f(x) = g(x)$?
5. How does composition of functions relate to transformations of graphs?

Tip: Always double-check substitution and simplification steps to avoid errors in composition!