2.1 Functions

Lecture

• Part 1
• Part 2
• Part 3

Lecture notes

1. How do you read $D=\{\forall x|x\in \Re ,x\neq -5\}$?

Answer: ${\begin{aligned}\overbrace {D} ^{\text{the domain}}\underbrace {=} _{\text{is}}\overbrace {\{} ^{\text{the set}}\underbrace {\forall x} _{\text{of all x}}\overbrace {|} ^{\text{such that}}\underbrace {x\in \Re } _{\text{x is an element of the real number set}}\overbrace {,x\neq -5} ^{\text{where x is not equal to -5}}\end{aligned}}$

2. How do you covert from radical form to exponential form?

Answer: ${\begin{aligned}{\sqrt[{m}]{(x)^{n}}}=\left({\sqrt[{m}]{x}}\right)^{n}=x^{\frac {n}{m}}\end{aligned}}$ Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle m} is called the index and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle n} is called the power.

\left ( \frac{1}{2} \right )^n