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:

📰 KWWL News Exposes the Biggest Scandal in Local Politics—See Whats Unfolded Today! 📰 Breaking: KWWL News Sparks National Debate with Controversial New Report! 📰 You Wont Believe What KXAN Radar Actually Detects—Shocking Tech Revolution! 📰 Aa Customer Service Contact 2941295 📰 This 1A Hair Breakthrough Is Taking The Beauty World By Storm 5077075 📰 Game Not Blocked Discover The Ultimate Bypass For Unrestricted Play Now 2818440 📰 Film Martin Sheen 4870411 📰 Get A Business Loan 1928953 📰 Substituting These Into The Combination Formula 7725977 📰 Secrid Secrets That Will Make You Question Everything 7559960 📰 Nimedes Exposed The Hidden Secrets That Shocked The Entire Industry 7542648 📰 Rob Riener 4604600 📰 U Need Permission From Trustedinstaller 6006640 📰 Master Division In Excel Faster With This Secret Formula 7742950 📰 Guard Your Wifithis Trouble Accessing Internet Issue Ruins Every Few Minutes 8869093 📰 Virginia Permit Practice Test 7274621 📰 Learn How To Install Instantly In Minutesonly With Our Step By Step Guide 5843887 📰 Lockheed Martin Surpasses Yahoo Finance Shock Driven Breakthrough In Defense Stocks 522989

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.