Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem defines two functions, $f(x) = x^2 - 1$ and $g(x) = 3x + 2$. Part (a) asks us to simplif...
FunctionsFunction CompositionInverse FunctionsOne-to-one Functions
2025/3/25
The problem provides two functions, $f(x) = 2x + 3$ and $g(x) = (x+2)^2 - 1$. We are asked to find ...
Function CompositionPolynomialsFunction Evaluation
2025/3/25
We are given a function $g(x) = \frac{2x+3}{3x-1}$ defined for $x \neq \frac{1}{3}$. We need to find...
FunctionsInverse FunctionsAlgebraic Manipulation
2025/3/25
Given the functions $f(x) = \frac{2x - 1}{2}$ and $g(x) = x - 4$, find the value of $x$ when $f(x) =...
FunctionsLinear EquationsSolving Equations
2025/3/25
The problem asks to match each of the six given inequalities to the graph that represents its soluti...
InequalitiesLinear InequalitiesSolving InequalitiesGraphing Inequalities
2025/3/25
The problem asks us to fill in the boxes with positive integers from 1 to 9, using each integer at m...
InequalitiesInteger EquationsProblem Solving
2025/3/25
The problem describes the constraints on a student's work hours and earnings at a college. Students ...
InequalitiesWord ProblemsLinear InequalitiesConstraints
2025/3/25
The problem describes a scenario where a principal is hosting a luncheon with a budget of $225. Each...
InequalitiesLinear EquationsWord ProblemsConstraints
2025/3/25
The problem defines a function $g(x) = \frac{3x}{1-x}$. We are asked to find two things: (i) The val...
FunctionsInverse FunctionsAlgebraic Manipulation
2025/3/25
The problem asks us to determine the number of solutions for the given system of equations: $y + \fr...
Systems of EquationsLinear EquationsSolutionsIdentical Equations
2025/3/25