You are asked to find $f(g(x))$ where:

• $f(x) = 3x - 5$
• $g(x) = 2x^2 - 5$

To find $f(g(x))$, we will substitute $g(x)$ into $f(x)$.

Steps:

1. First, recall that $f(x) = 3x - 5$.
2. Replace $x$ in $f(x)$ with $g(x)$: $f(g(x)) = 3(2x^2 - 5) - 5$
3. Now simplify the expression: $f(g(x)) = 3(2x^2 - 5) - 5 = 6x^2 - 15 - 5$ $f(g(x)) = 6x^2 - 20$

Thus, $f(g(x)) = 6x^2 - 20$.

Would you like more details on the steps or explanations?

Here are five related questions:

1. How do you find $g(f(x))$?
2. What is the general method for solving composite functions?
3. How would you determine the domain of $f(g(x))$?
4. Can composite functions be inverse functions of each other?
5. How can we graph $f(g(x))$?

Tip: Always simplify composite functions step-by-step to avoid mistakes.