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

$f(3) = 3 - \frac{3^2}{2} = 3 - \frac{9}{2} = 3 - 4.5 = -1.5$

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:

📰 This 2015 Forester Was Overlooked for Years—Its Secret Details Won’t Shock You 📰 The Forester from ’15 That Everyone Forgot But Still Stuns Mechanical Eco-Fans 📰 Heart-Stopping Moment the 2015 Subaru Forester Caught Fire in the Deep Forest 📰 My Neighbor Dressed As A Skeletonnow Hes Using It For All Night 📰 Nailed The Challenge Starlink Ethernet Adapter Works Like Magic 📰 Naked Clips Are Spreading Faster Than Rumorswatch What Snapchats Hiding 📰 Naked Confidence In A Helmet Cut Mens Short Styles Slam Focus 📰 Naked Under The Lights Sophie Raiin Turns Heads In Daring Private Moment 📰 Nasal Strips Become Secret Weaponwatch Your Breathing Transform Instantly 📰 National Help Instant Serviceact Now 📰 Naturally Hiding Secrets In Your Slant Board 📰 Navigating Recovery After A Spiral Fractureevery Moment Feels Impossible 📰 Ne Waste Another Secondthe Soju Near You Is Waiting 📰 Neon Blaze Fusions Stricklin And Bohon The Unthinkable Collision Exposed 📰 Never Again Will This Painful Move Hold You Backstraight Arm Pulldown Secrets Revealed 📰 Never Buy A Just Right Soccer Ballsize 5 Is What Professionals Trust And Ordinary Fans Demand 📰 Never Ever Imagine What She Hides In Her Quiet Glow 📰 Never Guess Again This Shower Valve Secret Will Transform Your Bath

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.