Inverse Functions

Inverse Functions

Definition of Inverse Functions $$ \Large+ \leftarrow \text{ inverse operation } \rightarrow -$$ $$ \Large \times \leftarrow \text{ inverse operation } \rightarrow \div $$ $$ \Large x^2 \leftarrow \text{ inverse operation } \rightarrow \sqrt{x} $$ The function $y=4x-1$ can be undone by its inverse function $y=\dfrac{x+1}{4}$. We can consider of this act as two processes [...]
Rational Functions

Rational Functions

We have seen that a linear function has the form $y=mx+b$. When a linear function is devided by another function, the result is a rational function. Rational functions are characterised by asymptotes, which are lines the function gets close and close to but never reaches. The rational functions we consider can be written in the [...]
Function Notation

Function Notation

Definition of Function Notation Consider the relation $y=3x+2$, which is a function. The $y$-values are determined from the $x$-values, so we say '$y$ is a function of $x$, which is abbreviated to $y=f(x)$. So, the rule $y=3x+2$ can be also be written as following. $$f: \mapsto 3x+2$$ $$\text{or}$$ $$f(x)=3x+2$$ $$\text{or}$$ $$y=3x+2$$ Function $f$ such that [...]