We are tasked with finding $(g \circ f)(4)$, which means evaluating the composition $g(f(4))$.

Given:

• $f(x) = x^2 - 3x + 3$
• $g(x) = 2x - 1$

Step 1: Find $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4) = 4^2 - 3(4) + 3 = 16 - 12 + 3 = 7$

Step 2: Find $g(f(4)) = g(7)$

Now substitute $x = 7$ into $g(x)$: $g(7) = 2(7) - 1 = 14 - 1 = 13$

Final Answer:

$(g \circ f)(4) = 13$

Would you like further explanation or details?

Here are some related questions:

1. What is $(f \circ g)(4)$?
2. How do you evaluate the composition of two functions in general?
3. Can you find $(g \circ f)(x)$ for any $x$?
4. How would this problem change if $g(x)$ were a different function?
5. What does the composition of functions represent graphically?

Tip: Always work step-by-step when evaluating compositions, starting from the inside function!