Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks us to find the gradient and y-intercept for each of the given linear equations. The...

Linear EquationsGradientY-interceptCoordinate Geometry

The problem asks us to find the gradient ($m$) and the y-intercept for each of the two given graphs ...

Linear EquationsGradientY-interceptCoordinate Geometry

The problem is to solve the following system of equations for $x$ and $y$: $x - y = 1$ $4 > x^2 - y^...

Systems of EquationsInequalitiesAlgebraic ManipulationDifference of Squares

We are given two sets of equations and asked to solve them. Set 1: $x^2 - y^2 = 3$ $x - y = 1$ Set 2...

Systems of EquationsQuadratic EquationsComplex NumbersDifference of Squares

We are given a system of two equations: $x^2 + y^2 = 5$ $x^2 + x^2 + 3y^2 = 14$, which simplifies to...

Systems of EquationsSubstitutionQuadratic Equations

The problem asks us to find the domain of the function $f(x) = \sqrt[5]{2x - 1}$.

DomainFunctionsRadicalsInequalities

Find the inverse of the function $f(x) = \sqrt{x^2 - 1}$.

Inverse FunctionsFunctionsSquare RootsDomain and Range

We are given two functions, $f(x) = 3x - 1$ and $g(x) = 2x^3$. We need to evaluate $f(g(-2))$.

Function CompositionAlgebraic Manipulation

We are given a matrix $A = \begin{pmatrix} 5 & a \\ -1 & -5 \end{pmatrix}$. We need to find the valu...

Matrix ExponentialsEigenvaluesTraceCharacteristic Equation

The problem asks which of the given sets $S_1$, $S_2$, and $S_3$ form a basis for $R^3$. $S_1 = \{(...

Linear AlgebraBasisVector SpaceDeterminantLinear Independence

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