Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given the inequality $\frac{m^2 - 20}{-(2m+5)} - \frac{m^2 + m - 12}{2m+5} < 2$ and the condi...

InequalitiesQuadratic EquationsRational ExpressionsInterval Notation

The problem asks to find $g(f(x))$ given the functions $f(x) = 3x^2 + 5$ and $g(x) = x - 1$. Also, t...

Function CompositionPolynomial FunctionsAlgebraic Manipulation

Given the functions $f(x) = 2x + 1$ and $g(x) = x^2 - 2$, the problem asks to find an expression inv...

Function CompositionFunctions

Given the functions $f(x) = x^2$ and $g(x) = 2x - 1$, we need to find (a) $g(f(x))$, which is the co...

FunctionsComposition of FunctionsAlgebraic Manipulation

The problem states that $F(x+2) = 2x^2 + 7x - 5$. We need to find the value of $F(-1)$.

FunctionsFunctional EquationsSubstitution

We are given the equation $\frac{x}{3} + \frac{x}{3} = 10$ and asked to solve for $x$.

Linear EquationsSolving Equations

The problem asks to find the maximum revenue for the revenue function $R(x) = 358x - 0.9x^2$. The an...

Quadratic FunctionsOptimizationVertex of a ParabolaRevenue FunctionCalculus (implicit)

The problem asks us to analyze the quadratic equation $y = 6 + 4x - x^2$. We need to find the vertex...

Quadratic EquationsParabolaVertexMaximum ValueOptimization

The problem is to solve the quadratic equation $7x^2 + 4 = 11x$ by factoring.

Quadratic EquationsFactoringSolving Equations

The problem asks to evaluate $(-8)^{\frac{2}{3}}$.

ExponentsRadicalsSimplification

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