1. Functions

Question 1

Sum function

Answer 1

(ƒ + g)(x) = ƒ(x) + g(x)

Question 2

Difference function

Answer 2

(ƒ – g)(x) = ƒ(x) – g(x)

Question 3

Product function

Answer 3

(ƒ • g)(x) = ƒ(x) • g(x)

Question 4

Quotient function

Answer 4

(ƒ / g)(x) = ƒ(x) / g(x)

g(x) ≠ 0

Question 5

Composition of functions

Answer 5

(ƒ o g)(x) = ƒ(g(x))

(g o ƒ)(x) = g(ƒ(x))

Question 6

The inverse of a function

(ƒ^-1 o ƒ)(x) = (ƒ o ƒ^-1)(x) = x

Answer 6

First write y in place of ƒ(x) and interchange x and y. Then solve for y and call the result ƒ^-1.

Since the domains and ranges of inverses are switched, the range of a function can be found by finding the domain of its inverse.

Question 7

Even function

Answer 7

ƒ(–x) = ƒ(x)

Outputs are equal for opposite inputs.

Symmetric about the y-axis.

Question 8

Odd function

Answer 8

ƒ(–x) = –ƒ(x)

Outputs are opposite for opposite inputs.

Symmetric about the origin.

Question 9

Relations

Answer 9

Association between two variables.

A set of ordered pairs: (x, y). x-vaules form domain and y-values form range.

Unlike functions, relations can be both odd and even.

Question 10

Sum of even functions or relations

Sum of odd functions

Product of two even or odd functions

Product of an even function and an odd function

Answer 10

is even.

is odd.

is even.

is odd.