Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

Given two functions $f(x) = 3\sqrt{x}$ and $g(x) = x^4 + 2$, we want to find the composite function ...

Function CompositionAlgebraic Functions

Find the domain of the function $f(x) = \frac{x-3}{\sqrt{x-5}}$.

FunctionsDomainRadicalsInequalities

Solve the equation $\frac{2x}{x-3} = 4 + \frac{6}{x-3}$.

Algebraic EquationsRational EquationsSolving EquationsNo Solution

We need to solve the equation $\frac{2x}{x-3} = 4 + \frac{6}{x-3}$ for $x$.

Rational EquationsSolving EquationsNo Solution

The problem asks us to solve the equation $3(x - 9) = 4 - 2(x + 2)$ for $x$.

Linear EquationsSolving EquationsVariable Isolation

The problem asks us to simplify the expression $3(4x-5)+2$.

Algebraic ExpressionsSimplificationDistributive PropertyLinear Equations

The problem states that $a$ varies directly as the square of $b$ and inversely as $c$. We are given ...

Direct and Inverse VariationProportionalityVariablesSolving Equations

The problem states that $a$ varies directly as the square of $b$ and inversely as $c$. We are given...

Direct VariationInverse VariationProportionalitySolving Equations

$a$ varies directly as the square of $b$ and inversely as $c$. Given that $a=2$ when $b=4$ and $c=24...

Direct VariationInverse VariationProportionalityAlgebraic Equations

The problem asks us to multiply the polynomial $(3a^3 + 5a^2 - a - 1)$ by the binomial $(a-7)$ and s...

PolynomialsMultiplicationSimplification

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