Function Compositions
What is a function compositions?
In Math, the composition of a function is an operation where two functions a new function.
What is dividing polynomials?
Dividing polynomials is an algorithm to solve a rational number that represents a polynomial divided by a monomial or another polynomial.
what is trigonometry?
Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
Who made the earliest fully developed base 10 numeration system?
Egyptians
What is a matrix?
A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Let f(x) = 2x + 3 and g(x) = x^2 - 1. Find the value of (f ∘ g)(2).
(f ∘ g)(2) = 9
What is synthetic division?
Synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
What is the value of sin(45 degrees)?
The value of sin(45 degrees) is √2 / 2.
Who is known as the "Father of Geometry"?
Euclid is known as the "Father of Geometry" for his work on Euclidean geometry, presented in his famous book called "Elements."
Multiply the matrices A = [[2, 3], [4, 1]] and B = [[5, 2], [0, 3]].
= [[10, 13], [20, 11]]
Let f(x) = sqrt(x) and g(x) = 2x + 1. Find the value of (g ∘ f)(9).
(g ∘ f)(9) = 7
Divide the polynomial (3x^3 + 2x^2 - 5x + 1) by (x - 2).
The quotient is 3x^2 + 8x + 11, and the remainder is 23.
Find the value of cos(π/3).
The value of cos(π/3) is 1/2.
Who created the four fundamental operations (addition, subtraction, multiplication and division)?
Find the determinant of the matrix C = [[3, 1], [4, 2]].
2
Let f(x) = 3x - 2 and g(x) = x^2 + 1. Find the value of (g ∘ f)(-1).
(g ∘ f)(-1) = 26.
Divide the polynomial (4x^4 - 7x^3 + 2x^2 - 5x + 3) by (x^2 - 3x + 2).
The quotient is 4x^2 - 5x + 4, and the remainder is 12x - 15.
Find the value of tan(π/4).
The value of tan(π/4) is 1.
Who is considered the founder of modern mathematics?
Many consider the French mathematician René Descartes to be the founder of modern mathematics due to his groundbreaking work in analytic geometry and the development of Cartesian coordinates.
Calculate the inverse of the matrix D = [[2, 1], [3, 4]].
[[4/5, -1/5], [-3/5, 2/5]]
Let f(x) = x^3 and g(x) = 1/x. Find the value of (f ∘ g)(2).
(f ∘ g)(2) = 1/8
Divide the polynomial 3x^3 + 5x^2 - 2x - 4 by x + 2 using synthetic division.
The quotient is 3x^2 - x + 2, and the remainder is 1.
What is the value of sec(60 degrees)?
The value of sec(60 degrees) is 2.
Who is credited with the development of calculus?
Sir Isaac Newton and Gottfried Wilhelm Leibniz are both credited with the development of calculus. They independently made significant contributions to the field during the late 17th century.
Find the inverse of the matrix A = [[3, 2], [1, 4]].
is [[2/5, -1/5], [-1/10, 3/10]].