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One feature that all of the examples listed above have in common is that, in each case, two or more known functions (sometimes multiplication by a constant, sometimes addition of two variables, sometimes the identity function) are inside the argument of the unknown functions to be solved for.
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
where x is a variable we are interested in solving for, we can use cross-multiplication to determine that x = b c d . {\displaystyle x={\frac {bc}{d}}.} For example, suppose we want to know how far a car will travel in 7 hours, if we know that its speed is constant and that it already travelled 90 miles in the last 3 hours.
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
Algebraic geometry is the study of the solutions in an algebraically closed field of multivariate polynomial equations. Two equations are equivalent if they have the same set of solutions. In particular the equation = is equivalent to =. It follows that the study of algebraic equations is equivalent to the study of polynomials.
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.