1. The problem is to understand the concept of a function in mathematics. 2. A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. 3. We denote a function as $f(x)$, where $x$ is the input and $f(x)$ is the output. 4. For example, if $f(x) = 2x + 3$, then for each value of $x$, we calculate $f(x)$ by multiplying $x$ by 2 and then adding 3. 5. This means if $x=1$, then $f(1) = 2(1) + 3 = 5$. 6. Functions can be represented in various ways: equations, tables, graphs, or mappings. 7. The key property is that each input $x$ has exactly one output $f(x)$, ensuring the function is well-defined. 8. Understanding functions is fundamental in algebra and many areas of mathematics and science.