Final answer:
To find the inverse of an equation, such as x + y = 7, you subtract x from both sides, giving you y = 7 - x. This method is essential in algebra for isolating a variable and understanding function properties, like even and odd functions, and handling expressions with negative exponents.
Step-by-step explanation:
To find the inverse of the equation x + y = 7, you can subtract x from both sides to isolate the variable y. This results in the inverse equation y = 7 - x. When solving for a single variable, it's important to perform the same operation on both sides of the equation to maintain the equality. For example, if we have the operation 5 - (+3) = 5 - 3 = 2, we note that the sign of the number being subtracted is changed before performing the addition.
Manipulating equations is a fundamental skill in algebra, which is necessary when you have an expression with more than one variable, like 7y = 6x + 8, and you need to solve for one variable. It also applies when working with functions and understanding their properties, such as even and odd functions. Reflecting a function over an axis is an example of how we can visually understand these types of functions, such as the symmetry of an even function about the y-axis, where y(x) = −y(-x).
In the context of functions and algebra, it's also essential to understand how to handle expressions involving powers, like x^(-n) = 1/x^n. This is indicative of how negative exponents represent the reciprocal of the base raised to the positive exponent. These algebra techniques also extend to work with vectors and scalar subtraction, where we follow similar principles.