Evaluating Mathematical Functions and Simplifying Expressions

Diving into basic mathematical operations, this article aims to explain the process of evaluating mathematical functions, focusing on the notation and arithmetic involved. We will break down the given problem step-by-step, enhancing your understanding of function evaluation, arithmetic simplification, and their applications.

Evaluating Mathematical Functions: A Brief Overview

Mathematical functions are fundamental tools in various fields, from calculus to engineering. Understanding how to evaluate a function is crucial for solving more complex problems. This article will walk you through an example problem using the given functions f(x) 2x and g(x) x1, demonstrating the process of function evaluation and simplification.

Function Evaluation with Given Functions

Let's consider the given functions:

f(x) 2x g(x) x1

The problem requires us to compute f-2 g1. This expression involves evaluating each function at specific points and then performing the necessary arithmetic operations. Let's break it down.

Evaluating f-2

The notation f-2 suggests evaluating f(x) at x -2. Plugging in -2 into the function f(x) 2x, we get:

f(-2)  2(-2)  -4

Thus, f-2 -4.

Evaluating g1

The notation g1 suggests evaluating g(x) at x 1. Plugging in 1 into the function g(x) x1, we get:

g(1)  11  2

Thus, g1 2.

Combining the Results: f-2 g1

Now that we have evaluated both functions, we can combine the results to find f-2 g1. The expression f-2 g1 can be interpreted as multiplying the results of f-2 and g1:

f-2 g1  (-4) times; 2  -2

Hence, the result of the expression f-2 g1 is -2.

Substituting and Evaluating Step-by-Step

To further clarify the process, let's break down the substitution and evaluation step-by-step:

Substitute the value of the point at which we compute the function into f(x) 2x and g(x) x1. Evaluate f(-2) 2(-2) -4. Evaluate g(1) 11 2. Multiply the results: -4 times; 2 -2.

This systematic approach helps ensure that the arithmetic is correct and the steps are easily traceable.

Conclusion

Evaluating mathematical functions and simplifying expressions are foundational skills in mathematics. Whether you're working on calculus problems or solving real-world applications, a clear understanding of these concepts is vital. The process of function evaluation, as demonstrated in this article, involves careful substitution, step-by-step arithmetic, and the application of basic mathematical rules. By mastering these steps, you can tackle more complex mathematical challenges with confidence.

References

For further reading, consult introductory texts on algebra and calculus. Popular textbooks include 'Algebra and Trigonometry' by James Stewart and 'Calculus: Early Transcendentals' by Jon Rogawski. Online resources like Khan Academy provide comprehensive tutorials and exercises to help deepen your understanding.