To find $f(5)$, we substitute $x = 5$ into the function $f(x) = (3x - 2)^2$:

$f(5) = (3(5) - 2)^2$

Simplify inside the parentheses:

$3(5) = 15, \quad \text{and} \quad 15 - 2 = 13$

Now square the result:

$f(5) = 13^2 = 169$

Final Answer:

$f(5) = 169$

Would you like details on any part of this computation? Here are 5 related questions to explore:

1. What is $g(5)$ if $g(x) = 4x + 3$?
2. How do you find $(f \circ g)(x)$ or $(g \circ f)(x)$ for these functions?
3. What is $f'(x)$, the derivative of $f(x) = (3x - 2)^2$?
4. Can $g(x)$ and $f(x)$ intersect? If so, how would you solve $f(x) = g(x)$?
5. How does squaring a linear function affect the shape of its graph?

Tip:

Always simplify the innermost expressions first when evaluating functions to avoid errors!