Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We need to find the domain of the function $f(x) = \frac{x^2}{3 - 4x^4}$. The domain of a rational f...

FunctionsDomainRational FunctionsExponentsRadicals
2025/6/9

The problem provides a table showing the current month's incoming amount, consumption amount, and in...

Linear EquationsInequalitiesWord Problem
2025/6/8

The problem is to simplify the expression $(2x^{-1}y^{-2}z^{-3})^{-2} \times (3x^{-2}y^{-3}z^{-1})^3...

ExponentsSimplificationAlgebraic Expressions
2025/6/8

The general term of a sequence is given by $T_n = \frac{n(n+1)}{2}$. We need to find the value of $T...

Sequences and SeriesArithmetic SequencesFormula ApplicationEvaluation
2025/6/8

The problem asks us to add two complex numbers, $3-2i$ and $4+3i$, and then multiply the result by t...

Complex NumbersComplex Number ArithmeticImaginary Numbers
2025/6/8

Solve the inequality $2(5 - 3x) - 4x + 6 \ge 0$ for $x$.

InequalitiesLinear InequalitiesAlgebraic Manipulation
2025/6/8

The problem asks us to solve the quadratic equation $x^2 + 6x + 9 = 0$ by factorization and describe...

Quadratic EquationsFactorizationRoots of EquationsDiscriminant
2025/6/8

The problem asks to find the domain of the expression $\frac{x}{x+7}$. The domain is the set of all ...

DomainRational ExpressionsInequalities
2025/6/8

The question asks us to identify the type of function whose range consists of only one element. The ...

FunctionsRangeConstant FunctionOne-to-one FunctionOnto Function
2025/6/8

The problem asks us to solve two equations. The first equation is $-5(a-3) = -2a$ for $a$. The secon...

Linear EquationsSolving EquationsAlgebraic ManipulationFractions
2025/6/8