# Tagged Questions

Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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### How to approach general solutions to functional equations of multiple variables

I understand the concept of a function, broadly speaking, but when it comes down to solving general functional equations, I sometimes find it difficult to wrap my head around the problem at hand. For ...
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### Bound on $c-b$ for $a^n+b^n=c^n$

Let $a\leq b\leq c$ be positive real numbers and $n$ positive integer with $a^n+b^n=c^n$. Prove that $c-b\leq(\sqrt[n]{2}-1)a$. The desired inequality can be written as $c-b+a\leq \sqrt[n]{2}a$. ...
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### Algebra and summation question

${(1+\frac{q_jr^i}{1-q_j})}^{-1}=\sum_{k=1}^{\infty} (-1)^{k-1}(\frac{q_jr^i}{1-q_j})^{k-1}$ What rule is being used to go from the LHS to the RHS? My knowledge in maths is first year undergrad, but ...
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