1.2. Functions summary, Lecture notes of Mathematics

Download 1.2. Functions summary and more Lecture notes Mathematics in PDF only on Docsity!

PURE 2. Functions * numbers review ein Rnlaentls object —> image range domain —> . —- fin >atad , ER oR f(x) = x+ 25; xéR Natural numbers No leg. 4.2.3) Tneges Z (eg-: -3,-a,-4,0, 4,8,3 Rational numbers Q (a2 = anything splayed as. Faction’ ons alt 1) ) Real numbers R = all rational + rational #3 (eg.: 1a, input —> output 2. Composite functions = combination of 22 funchons Page a) 7 Rangaat +9 “im general, 40g) # gil) + file) = fimetion applied wice- Find ind fla) 3. Tnverse. finetions = undoes what the imction does Fa) 2 FF) £0 5 2 the domain of $C) 13 the range of f6e) i» + the range of fC) is the domaun of f(x) | fa) * not every function. has. an inverse Ne % only if fle) is a one-one mapping does #74) exist £"G) domain of F range of F eg: {lx)s 5x-4 . Fird fle) # 4) White fimetion os — y+ het (a 2) Triercharge, % and — pod { 5 | 3) Rearrange , make » subject > ys aed \ 3s / P 5 Es Pees — a PG) et range of F domain of 4. Graphs of functions and its inverse. = reflections of each other over the line yor + if Fis self- inverse, fie)* FG) { eg: f= 2 =F { x / goph of F 1s symmetrical about the line yo x * combining transformations yo eF 2a 3 * Q vertical transformations #lx) — * Q horizontal ‘transformations fi.) — stretch }, factor % rmutiply #02) by translate ( :) 0 & replace x with +0 + Fox) faa) + t-oxis translate. (0 — af) (3) > a fadtk & add & + fl.) shetch <> , factor 4 — flxtc)—> b \_, (bn +e) & replace x with ox * c switches (+1-) na) + b switches (x /=)