g(3) = 3^2 - 4(3) + 5 = 9 - 12 + 5 = 2
Understanding g(3) = 3² – 4(3) + 5 and Why It Equals 2: A Clear Step-by-Step Breakdown
When evaluating expressions like g(3) = 3² – 4(3) + 5, it’s essential to follow the correct order of operations to arrive at the accurate result. This process not only ensures mathematical precision but also enhances understanding of algebraic evaluation—an essential skill in math and STEM education.
In this article, we’ll walk through the step-by-step calculation of g(3) = 3² – 4(3) + 5, explain why evaluating the expression correctly leads to 2, and discuss the importance of following the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
What Does g(3) Mean?
In mathematics, g(x) is a function defined by the expression g(x) = x² – 4x + 5. Evaluating g(3) means substituting x = 3 into the function and simplifying accordingly.
Step 1: Substitute x = 3
Start by replacing every instance of x with 3 in the expression: g(3) = 3² – 4(3) + 5
Step 2: Follow the Order of Operations (PEMDAS)
Now simplify the expression step-by-step:
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Evaluate exponents first: 3² = 9 So the expression becomes: g(3) = 9 – 4(3) + 5
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Perform multiplication next: 4 × 3 = 12 Now: g(3) = 9 – 12 + 5
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Carry out subtractions and additions from left to right:
- First: 9 – 12 = -3
- Then: -3 + 5 = 2
Final Result:
g(3) = 2
Why This Matters: The Role of Correct Order of Operations
Many students mistakenly perform operations out of sequence—like subtracting before multiplying or adding before multiplying—which leads to incorrect answers. Using PEMDAS ensures consistent, accurate computation, making it indispensable in algebra, calculus, computer science, and engineering.
Moreover, clearly understanding each step enhances mathematical fluency and prepares learners for more complex functions and equations.
Summary
- Substitution: g(3) = 3² – 4(3) + 5
- Exponents first: 3² = 9
- Multiplication: 4 × 3 = 12
- Then subtraction/addition (left to right): 9 – 12 + 5 = 2
- Final result: g(3) = 2
This simple yet critical function evaluation illustrates how basic algebra builds a foundation for higher-level math and problem-solving.
Practice Tip
Strengthen your skills by practicing function evaluation with different values. Try:
- What is g(2)?
- What is g(0)?
- What is g(–1)?
Each provides valuable opportunities to apply the same principles and deepen understanding.
Understanding and correctly evaluating expressions like g(3) = 3² – 4(3) + 5 confirms mathematical accuracy and supports lifelong learning in STEM fields. Keep practicing, and soon the order of operations will become second nature!
