1. Functions and Differentiation

Question 1

Domain

Answer 1

Set on which a function is defined

Question 2

Codomain

Answer 2

Set on which output of f(x) is constrained to fall

Question 3

Range

Answer 3

Set of elements of Y associated with elements of x

Question 4

Composite function

Answer 4

A function whose argument is itself a function z=g(f(x))

Question 5

Inverse functions

Answer 5

Given y=f(x) sometimes we may want to write its inverse, x=f^-1(y)

Question 6

When does an inverse function exist?

Answer 6

Only for one to one functions I.e. the original function is strictly monotonic

Question 7

When is a function continuous?

Answer 7

If it’s graph has no breaks in it

Question 8

What shape is a concave function?

Answer 8

n shaped

Question 9

What shape is a convex function?

Answer 9

U shaped

Question 10

What is the differential of e^x?

Answer 10

e^x

Question 11

What is the differential of ln(x)?

Answer 11

1/x

Question 12

Product rule formula

Answer 12

Y’= u’v + uv’

Question 13

Quotient rule formula

Answer 13

Y’=(u’v + uv’)/v^2

Question 14

Chain rule formula

Answer 14

When y=u(v)
Y’=v’ x u’(v)

Question 15

How else can 3^x be written?

Answer 15

e^(xln3)

Question 16

How can the second derivative determine concavity/convexity?

Answer 16

f”(x)>0 convex
f”(x)<0 concave

Question 17

What is a^(loga(x)) equal to?

Answer 17

X

Question 18

How else can log(xy) be written?

Answer 18

Log(x) + log(y)

Question 19

How else can log(x)- log(y) be written?

Answer 19

Log(x/y)

Question 20

How else can log(x^p) be written?

Answer 20

Plog(x)

Question 21

What is loga(a) equal to?

Answer 21

1

Question 22

How else can loga(x)/loga(b) be written?

Answer 22

Logb(x)