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.

Understanding the Context

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

$=\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+\frac{9}{2}+\frac{3}{2}$

Image Gallery

$=\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+\frac{9}{2}+\frac{3}{2}$

Ex 2.3, 3 - f(x) = 2x - 5. Write down f(0), f(7), f(-3) - Class 11

Key Insights

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

🔗 Related Articles You Might Like:

📰 Free to Play Computer Games 📰 Fortnite Parental Controls How to Turn Off 📰 Warhammer 3 Dlc 📰 From Anonymous Heroes To Legendary Agents Discover The Cast Of Shield Now 4025399 📰 Thread Java 📰 You Wont Believe The Crazy Way To Eat Edamame For Instant Energy 3634186 📰 1500 Dollar Check Direct Deposit 2025 3234633 📰 This Reconciliation Act Is Secrets Behind Work Reformsyour Future Job Depends On Understanding It Now 2068084 📰 Leo Persicas Dark Past Exposedwhat He Never Spoke About Will Astound You 9031588 📰 Microsoft Office 2008 For Mac Download 📰 Lou Holtz 1034193 📰 Verizon Wireless Morehead City 📰 Quanti Research 5453151 📰 Hilton Grand Waikikian 3774650 📰 Tweetbot For Ios 📰 Lego Star Wars The Complete Saga Codes 📰 The Roses You Never Knew Were Watching Every Morning Light 7907755 📰 Sources Say Michael Jackson Xscape And The Outcome Surprises

Final Thoughts

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.