Algebra multiplication involves multiplying variables and/or constants together. The general format for algebra multiplication is: a * b where “a” and “b” can be any combination of numbers or variables. For example: 2 * 3 = 6 x * y = xy When multiplying variables together, we can use the rules of exponents to simplify…
Algebra addition refers to the mathematical operation of combining two or more numbers or variables to get a sum. In algebra, addition is usually denoted by the plus sign (+). For example, if we have two variables, x and y, we can add them together using the expression “x + y”. The addition of numbers…
Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as i^2 = -1. The algebraic operations on complex numbers are similar to those of real numbers. We can add, subtract, multiply and divide complex numbers. Addition: To add…
Product of Functions: The product of two functions f(x) and g(x) is denoted by f(x) * g(x) and is defined as (f * g)(x) = f(x) * g(x) for all x in the domain of both f and g. For example, if f(x) = x^2 and g(x) = sin(x), then (f * g)(x) = x^2…
The greatest integer function, denoted by ⌊x⌋ or sometimes by [x], is a mathematical function that returns the largest integer that is less than or equal to its argument x. For example, ⌊4.5⌋ = 4 and ⌊-2.7⌋ = -3. Formally, the greatest integer function is defined as follows: For any real number x, let n…
The absolute value of a real number is the distance of the number from zero on the number line. It is denoted by two vertical bars surrounding the number, like |x|. More formally, the absolute value of a real number x is defined as: |x| = x, if x is greater than or equal to…
Power can refer to a variety of things depending on the context in which it is used. Here are a few possible interpretations: What is Required power Required power refers to the amount of power needed to perform a specific task or achieve a particular goal. In engineering and mechanics, required power is often calculated…
Logarithmic refers to a mathematical concept related to the logarithm function. The logarithm function is the inverse of the exponential function and is used to express the relationship between numbers in terms of their powers. In other words, the logarithm of a number is the power to which another fixed number, called the base, must…
Onto and one-to-one are both terms used to describe functions in mathematics. An onto function (also called a surjective function) is a function in which every element in the range is mapped to by at least one element in the domain. In other words, for every element y in the range, there exists at least…
Even and odd functions are two types of functions defined in mathematics. An even function is a function f(x) that satisfies the following property: f(-x) = f(x) for all x in the domain of the function. In other words, if you reflect the graph of an even function about the y-axis, the result is the…