To find the composition of the functions $f$ and $g$, denoted as $(f \circ g)(x)$, you need to substitute $g(x)$ into $f(x)$.

Given:

• $f(x) = 2x - 9$
• $g(x) = -x + 4$

Now, calculate $(f \circ g)(x)$: $(f \circ g)(x) = f(g(x))$ Substitute $g(x) = -x + 4$ into $f(x)$: $f(g(x)) = f(-x + 4)$ Now, replace $x$ in $f(x) = 2x - 9$ with $-x + 4$: $f(-x + 4) = 2(-x + 4) - 9$ Distribute and simplify: $f(-x + 4) = -2x + 8 - 9$ $f(-x + 4) = -2x - 1$

So, the composition $(f \circ g)(x) = -2x - 1$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you find $g \circ f(x)$?
2. What is the value of $(f \circ g)(2)$?
3. How do you find the inverse of $f(x)$?
4. What is the domain of the function $f \circ g(x)$?
5. How do you graph the function $f \circ g(x)$?

Tip: When composing functions, always replace the entire variable in the outer function with the expression from the inner function.