To find $(f \circ g)(x)$, which is $f(g(x))$, we substitute $g(x)$ into $f(x)$.

Given:

• $f(x) = 5x - 4$
• $g(x) = 10x - 8$

We need to calculate: $(f \circ g)(x) = f(g(x)) = f(10x - 8)$

Now substitute $g(x)$ into $f(x)$: $f(10x - 8) = 5(10x - 8) - 4$

Simplify: $f(10x - 8) = 5(10x) - 5(8) - 4 = 50x - 40 - 4 = 50x - 44$

Thus: $(f \circ g)(x) = 50x - 44$

Would you like more details on the composition of functions or have any questions?

Here are five related questions to further your understanding:

1. What is the process for finding $(g \circ f)(x)$?
2. How would you find $(f \circ f)(x)$?
3. Can you explain the difference between function composition and multiplication?
4. How would the process change if the functions were not linear?
5. How would you interpret the graph of $(f \circ g)(x)$ in comparison to $f(x)$ and $g(x)$?

Tip: When composing functions, always ensure to substitute the inner function completely before simplifying the expression.