Chapter 5: Q. 73 (page 269)

Use the graph of $y = f (x)$ given in the Problem $43$ to evaluate the following:
(a) $f (- 1)$
(b) $f (1)$
(c) $f^{- 1} (1)$
(d) $f^{- 1} (2)$

Short Answer

Expert verified

According to the graph of $f (x)$ and its inverse

(a) $f (- 1) = 0$

(b) $f (1) = 2$

(d) $f^{- 1} (2) = 1$

Step by step solution

Step 1. Given data

The given graph is

Step 2. Graph of the inverse function

Points on the graph of the function $f (x)$ are

$(- 2, - 2), (- 1, 0), (0, 1), & (1, 2)$

then the points of the function $f^{- 1} (x)$ will be

$(- 2, - 2), (0, - 1), (1, 0), & (2, 1)$

So the graph of the inverse function is

Step 3. Part (a)

From the graph

$(- 1, 0)$ is a point on the graph of $f (x)$

sorole="math" localid="1646167799685" $f (- 1) = 0$

Step 4. Part (b)

From the graph

$(1, 2)$ is a point on the graph of $f (x)$

sorole="math" localid="1646167820149" $f (1) = 2$

Step 5. Part (c)

From the graph

$(1, 0)$ is a point on the graph of $f^{- 1} (x)$

so $f^{- 1} (1) = 0$

Step 6. Part (d)

From the graph

$(2, 1)$ is a point on the graph of $f^{- 1} (x)$

so $f^{- 1} (2) = 1$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use the graph of $y = f (x)$ given in the Problem $43$ to evaluate the following:
(a) $f (- 1)$
(b) $f (1)$
(c) $f^{- 1} (1)$
(d) $f^{- 1} (2)$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Graph of the inverse function

Step 3. Part (a)

Step 4. Part (b)

Step 5. Part (c)

Step 6. Part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the graph of y=f(x)given in the Problem 43to evaluate the following:(a) f(-1)(b) f(1)(c) f-1(1)(d) f-1(2)

Short Answer

Step by step solution

Step 1. Given data

Step 2. Graph of the inverse function

Step 3. Part (a)

Step 4. Part (b)

Step 5. Part (c)

Step 6. Part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the graph of $y = f (x)$ given in the Problem $43$ to evaluate the following:
(a) $f (- 1)$
(b) $f (1)$
(c) $f^{- 1} (1)$
(d) $f^{- 1} (2)$