To solve $(f \circ g)(x)$, which is the composition of the functions $f(x) = 3x - 5$ and $g(x) = x - 9$, follow these steps:

Step 1: Understand function composition.

The composition $(f \circ g)(x)$ means that we apply $g(x)$ first, and then use the result as the input to $f(x)$. In other words: $(f \circ g)(x) = f(g(x))$

Step 2: Substitute $g(x)$ into $f(x)$.

Since $g(x) = x - 9$, substitute this expression into $f(x)$: $f(g(x)) = f(x - 9)$

Now, recall that $f(x) = 3x - 5$. Replace $x$ in $f(x)$ with $x - 9$: $f(x - 9) = 3(x - 9) - 5$

Step 3: Simplify the expression.

Simplify the expression: $3(x - 9) - 5 = 3x - 27 - 5 = 3x - 32$

Thus, the expression equivalent to $(f \circ g)(x)$ is: $(f \circ g)(x) = 3x - 32$

Would you like more details or have any questions?

Related Questions:

1. What would $(g \circ f)(x)$ look like with the same functions?
2. How do you evaluate $(f \circ g)(2)$?
3. What happens if you change the functions to non-linear forms, like $f(x) = x^2$?
4. Can you find the domain of the composed function $(f \circ g)(x)$?
5. How would this composition work if $g(x)$ was a trigonometric function?

Tip:

When performing function composition, always start by substituting the inner function's output as the input to the outer function, and carefully simplify the result.