Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem is to solve question 13: If $f(x) = x^3$, find the value of $\frac{f(5) - f(1)}{5-1}$.
FunctionsPolynomialsEvaluation
2025/5/6
We are given a system of two equations: $x^2 + y^2 = 40$ $x^2 - y^2 = 10$ We need to solve for $x$ a...
Systems of EquationsQuadratic EquationsSolving Equations
2025/5/6
The problem consists of multiple parts. We need to solve the problems from question 7 to 13 from the...
FunctionsFunction EvaluationFunction PropertiesTrigonometric Identities
2025/5/6
We are given the function $f(x) = \frac{x-1}{x+1}$. We need to prove that $f(2x) = \frac{3f(x)+1}{f(...
Function PropertiesFunction CompositionAlgebraic Manipulation
2025/5/6
The problem is to solve the equation $0 - 4 = \frac{1}{4}y$ for $y$.
Linear EquationsSolving Equations
2025/5/6
We are given the equation $0-4 = -\frac{1}{4}^y$ and we want to solve for $y$.
ExponentsEquationsSolving EquationsAlgebraic Manipulation
2025/5/6
The problem asks us to find $f(x-1)$ given the function $f(x) = 3x^4 - 5x^2 + 9$.
PolynomialsFunction TransformationAlgebraic ManipulationSubstitution
2025/5/6
The problem asks to compute the scalar multiplication of a matrix. We are given $M = \frac{1}{3} \b...
Linear AlgebraMatrix MultiplicationScalar MultiplicationMatrices
2025/5/6
The problem gives a matrix $R = \begin{bmatrix} 2 & 1 \\ -3 & 4 \end{bmatrix}$ and asks to compute s...
MatrixDeterminant2x2 Matrix
2025/5/6
We need to solve the equation $4y - 2y = 16$ for the variable $y$.
Linear EquationsSolving Equations
2025/5/6