The problem asks to evaluate $(f \circ g)(3)$, which is the composition of the two functions $f(x)$ and $g(x)$, without finding an explicit equation for the composition.

Given:

• $f(x) = 5x - 3$
• $g(x) = 2x - 7$

We need to follow these steps:

1. First, evaluate $g(3)$ by substituting $x = 3$ into the equation for $g(x)$: $g(3) = 2(3) - 7 = 6 - 7 = -1$

2. Next, use the result $g(3) = -1$ as the input for the function $f(x)$. So now, we evaluate $f(-1)$: $f(-1) = 5(-1) - 3 = -5 - 3 = -8$

Therefore, $(f \circ g)(3) = -8$.

Let me know if you'd like more details or have further questions.

Here are 5 related questions for practice:

1. What is $(g \circ f)(3)$ using the same functions?
2. What is $g(f(2))$ with the same given functions?
3. How do you find the inverse of $f(x) = 5x - 3$?
4. How do you determine if $f \circ g$ is a one-to-one function?
5. Can you describe the steps to graph the composition $f(g(x))$?

Tip: When working with function compositions, always evaluate the inner function first, then substitute its output into the outer function.