Inverse Functions

Inverse Functions

Home > 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 [...]
Rational Functions

Rational Functions

Home > 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 [...]
Function Notation

Function Notation

Home > Functions 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 [...]