math 2: functions

Question 1

unless explicitly stated, the domain of a function is

Answer 1

all real values that produce real numbers as solutions

Question 2

in a relation, unlike a function, a particular input number might be paired with

Answer 2

more than one output number

Question 3

sum function→

Answer 3

(f+g)(x)= f(x) + g(x)

Question 4

difference function→

Answer 4

(f-g)(x)= f(x) - g(x)

Question 5

product function→

Answer 5

(f x g)= f(x) x g(x)

Question 6

quotient function→

Answer 6

(f/g)(x) = f(x)/ g(x); g(x) ≠ 0

Question 7

composition of functions→

Answer 7

(f ∘ g)(x)= f(g(x))

g ∘ f)(x)= g(f(x)

Question 8

to confirm if a function is an inverse of another function (rule)

Answer 8

( f^-1 ∘ f)(x) = (f ∘ f^-1)(x) = x

Question 9

if the inverse of a function is not a function, it can be made into a function by

Answer 9

limiting the domain

Question 10

since the domains and ranges of inverses are switched, the range of a function can be found by finding the

Answer 10

domain of the inverse

Question 11

a relation is even if (-x, y) is in the relation whenever

Answer 11

(x, y) is

Question 12

a relation is odd if (-x, -y) is in the relation whenever

Answer 12

(x, y) is

Question 13

sum of even functions is

Answer 13

even

Question 14

sum of odd functions is

Answer 14

odd

Question 15

product of 2 even or odd functions is

Answer 15

even

Question 16

product of an even with an odd function is

Answer 16

odd