Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks us to find the inverse function $f^{-1}(y)$ given the function $f(x) = 8(x-2) + 4$.
Inverse FunctionsLinear FunctionsFunction Transformation
2025/7/3
The problem asks us to find the solution of the exponential equation $15e^x - 9 = 18$ in terms of lo...
Exponential EquationsLogarithmsEquation Solving
2025/7/3
The problem states that a vehicle purchased for $20700 depreciates at a constant rate of 13% each ye...
Exponential DecayLogarithmsModelingEquationsDepreciation
2025/7/3
The problem asks to find the inverse of the function $f(x) = \log_3(x+2)$.
FunctionsInverse FunctionsLogarithmsExponentials
2025/7/3
We are asked to solve the equation $5(7)^x = 118$ for $x$ and round the answer to two decimal places...
Exponential EquationsLogarithmsSolving EquationsApproximation
2025/7/3
We are asked to solve two equations: (a) $ln(x) = 2$ (b) $e^{x+7} = 4$
LogarithmsExponentialsEquations
2025/7/3
We are given that the function $f$ is a one-to-one function. (a) We are given that $f(6) = 9$, and w...
FunctionsInverse Functions
2025/7/3
The problem is to simplify the expression $5^{\frac{1}{4}} \times 5^{\frac{1}{3}} \div 5^{\frac{1}{1...
ExponentsFractional ExponentsSimplification
2025/7/3
We are asked to find two functions $f(x)$ and $g(x)$ such that their composition $f(g(x))$ equals $\...
Function CompositionFunctions
2025/7/3
The problem asks us to find the function $g(x)$ such that $h(x) = (x+9)^6 = f(g(x))$, given that $f(...
Function CompositionPolynomialsAlgebraic Manipulation
2025/7/3