MTH 125 Calculus I

Course Info

• Section 02

• TR 9:30-11:10

• Prereq’s listed in detail on the syllabus

Personal Info

• Renea Randle

• Bachelors degree in Mathematices and Mechanical Engineering

• Masters in Mathematics.

Syllabus

SECTION 1.5 Inverse Functions

Inverse of a Function

Definition (p. 37)

A function is the inverse function of the function if

for all in the domain of

and

for all in the domain of

The function is denoted by (read “ inverse”).

Note

does NOT mean “ raised to the power of negative one.”

Pictorial Representation

Example 1

Show that the functions are inverses of each other.

and

Graphically . . .

Graphically . . .

𝑔 (𝑥 )= 5√ 𝑥+35

Graphically . . .

𝑦=𝑥

Inverses

Additional Properties of Inverses

• and are symmetric about the line .

• The domain of is the range of and the range of is the domain of.

• i.e. if (a, b) is a point on the graph of , then (b, a) is a point on the graph of .

The Existence of an Inverse Function (p. 39)

• A function has an inverse function if and only if it is one-to-one.

• Thus, graphically it will have to pass the horizontal line test.

Example 2

Which of the functions has an inverse?

a. b.

Finding the Inverse of a Function

To find the inverse of a given function . . .

1. Determine whether or not the function is invertible.

2. Switch the x’s and y’s.

3. Solve for y and rename it.

Example 3

Find the inverse of the function.

Inverse Trigonometric Functions

“Inverting” Trigonometric Functions

Formal Definitions

Inverse Trigonometric Properties

Example 4

Evaluate. (Be sure to put in radians!)

a. )

b.

c.

Example 5

Solve.

arccot

Example 6

Evaluate without a calculator.

a. arccos(cos )

b. cos(arcsec )

Example 7

Find csc given that arccos and .