Name:__________ warm-up 6-2

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find (f – g)(x), if it exists.

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find (f ● g)(x), if it exists.

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find [f ○ g](x), if it exists.

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find [g ○ f](x), if it exists.

To obtain a retail price, a dress shop adds $20 to the wholesale cost x of every dress. When the shop has a sale, every dress is sold for 75% of the retail price. If f(x) = x + 20 and g(x) = 0.75x, find [g ○ f](x) to describe this situation.

Let f(x) = x – 3 and g(x) = x2. Which of the following is equivalent to (f ○ g)(1)

A. f(1)

B. g(1)

C. (g ○ f)(1)

D. f(0)

Details of the DayEQ: How do radical functions model real-world problems and their solutions?

How are expressions involving radicals and exponents related?

I will be able to…

Find the inverse of a function or relation.

Determine whether two functions or relations are inverses.

Activities:Warm-upReview homeworkReview more questions from the MP ExamNotes: Inverse Functions and RelationsClass work/ HW

Vocabulary:

.

• inverse relation

• inverse function

6-2 INVERSE FUNCTIONS AND RELATIONS

Inverse

Functi

ons

and

Relations

The inverse of a function has all the same points as the original function, except that the x's and y's have been reversed.

A Quick Review Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find (f – g)(x), if it exists.

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find (f ● g)(x), if it exists.

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find [f ○ g](x), if it exists.

Using f(x) = 3x + 2 and g(x) = 2x2 – 1, find [g ○ f](x), if it exists.

A Quick Review To obtain a retail price, a dress shop adds $20 to the wholesale cost x of every dress. When the shop has a sale, every dress is sold for 75% of the retail price. If f(x) = x + 20 and g(x) = 0.75x, find [g ○ f](x) to describe this situation.

A Quick Review Let f(x) = x – 3 and g(x) = x2. Which of the following is equivalent to (f ○ g)(1)

A. f(1)

B. g(1)

C. (g ○ f)(1)

D. f(0)

Notes and examples

GEOMETRY The ordered pairs of the relation {(1, 3), (6, 3), (6, 0), (1, 0)} are the coordinates of the vertices of a rectangle. Find the inverse of this relation. Describe the graph of the inverse.

Notes and examplesGEOMETRY The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. What is the inverse of this relation?

Notes and examplesGEOMETRY The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. What is the inverse of this relation?

Notes and examples

Then graph the function and its inverse.

Step 4 Replace y with f –1(x).

Step 3 Solve for y.

Step 1 Replace f(x) with y in the original equation

Step 2 Interchange x and y.

Notes and examples

Graph the function and its inverse.

Notes and examples

Notes and examples

A. They are not inverses since [f ○ g](x) = x + 1.

B. They are not inverses since both compositions equal x.

C. They are inverses since both compositions equal x.

D. They are inverses since both compositions equal x + 1.