1. Functions and Differentiation Flashcards
Domain
Set on which a function is defined
Codomain
Set on which output of f(x) is constrained to fall
Range
Set of elements of Y associated with elements of x
Composite function
A function whose argument is itself a function z=g(f(x))
Inverse functions
Given y=f(x) sometimes we may want to write its inverse, x=f^-1(y)
When does an inverse function exist?
Only for one to one functions I.e. the original function is strictly monotonic
When is a function continuous?
If it’s graph has no breaks in it
What shape is a concave function?
n shaped
What shape is a convex function?
U shaped
What is the differential of e^x?
e^x
What is the differential of ln(x)?
1/x
Product rule formula
Y’= u’v + uv’
Quotient rule formula
Y’=(u’v + uv’)/v^2
Chain rule formula
When y=u(v)
Y’=v’ x u’(v)
How else can 3^x be written?
e^(xln3)
How can the second derivative determine concavity/convexity?
f”(x)>0 convex
f”(x)<0 concave
What is a^(loga(x)) equal to?
X
How else can log(xy) be written?
Log(x) + log(y)
How else can log(x)- log(y) be written?
Log(x/y)
How else can log(x^p) be written?
Plog(x)
What is loga(a) equal to?
1
How else can loga(x)/loga(b) be written?
Logb(x)
