f(3) = 3 - \frac{3^2}{2} = 3 - \frac{9}{2} = 3 - 4.5 = -1.5
Decoding f(3): A Simple Step-by-Step Evaluation of f(x) = 3 − 3²/2
Understanding how to evaluate mathematical expressions is a foundational skill in algebra and beyond. Today, we break down a specific function: f(3) = 3 − 3²⁄2, and walk through every step to arrive at the final answer of −1.5. This process not only clarifies a single problem but also strengthens key algebraic reasoning skills.
Breaking Down the Expression f(3) = 3 − 3²⁄2
At first glance, the expression f(3) = 3 − 3²⁄2 may look complex due to the combination of constant, exponentiation, and rational division. However, by following standard order-of-operations rules (PEMDAS/BODMAS), we simplify it step by step.
Step 1: Exponentiation — Evaluate 3²
In algebra, the symbol 3² means 3 squared, which equals 3 × 3 = 9. So, 3² = 9
Now substitute back: f(3) = 3 − 9⁄2
Step 2: Division — Evaluate 9⁄2
The expression now contains a division: 9 ⁄ 2. This is a proper fraction, representing 9 divided by 2, which equals 4.5 in decimal form. So, 9⁄2 = 4.5
Now the function becomes: f(3) = 3 − 4.5
Step 3: Subtraction — Final Computation
Subtracting a larger number from a smaller one gives a negative result: 3 − 4.5 = −1.5
Thus, f(3) = −1.5
Why Understanding f(3) Matters
While this function is simple, mastering such evaluations builds confidence in handling linear, quadratic, and rational expressions. Functions like f(x) form the backbone of higher mathematics—from calculus to computer science.
Understanding each operation’s place in the calculation chain helps prevent errors, especially when solving equations, analyzing graphs, or optimizing real-world problems.
Summary: The Full Calculation
| Step | Expression | Result | |-----------------------------|------------------------------|-------------| | Evaluate exponent | 3² | 9 | | Substitute & perform division | 3 − 9⁄2 | 3 − 4.5 = −1.5 | | Final answer | | f(3) = −1.5 |
Final Thoughts
Though f(3) = −1.5 may seem trivial, it reflects essential algebraic principles: clear order of operations, mastery of exponents, and confidence with fractions. These building blocks pave the way for tackling complex mathematical challenges with precision and clarity.
If you're studying functions, expressions, or algebra basics, practicing step-by-step simplification strengthens your problem-solving toolkit. Remember: every mathematical truth begins with a single, clear step.
Keywords: f(3) calculation, evaluate 3²/2, f(3) algebra, exponentiation step-by-step, understanding linear functions, division of decimals, algebraic operations, simplifying expressions, negative numbers in algebra
