Chapter 5: Q. 74 (page 269)

Use the graph of $y = f (x)$ given in Problem $44$ to evaluate
the following:
(a) $f (2)$
(b) $f (1)$
(c) $f^{- 1} (0)$
(d) $f^{- 1} (- 1)$

Short Answer

Expert verified

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

(a) $f (2) = \frac{1}{2}$

(b) $f (1) = 0$

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

Step by step solution

Step 1. Given data

Graph of $y = f (x)$ is

Step 2. Graph of the inverse function

Points on the graph of $y = f (x)$ are

$(- 2, - 2), (0, - 1), (1, 0), (2, 0.5)$

then the points on the inverse function $y = f^{- 1} (x)$ will be

$(- 2, - 2), (- 1, 0), (0, 1), (0.5, 2)$

So the graph of the inverse function is

Step 3. Part (a)

From the graph

$(2, \frac{1}{2})$ is a point on the graph of $y = f (x)$

sorole="math" localid="1646169175430" $f (2) = \frac{1}{2}$

Step 4. Part (b)

From the graph

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

so $f (1) = 0$

Step 5. Part (c)

From the graph

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

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

Step 6. Part (d)

From the graph

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

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

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Use the graph of $y = f (x)$ given in Problem $44$ to evaluate
the following:
(a) $f (2)$
(b) $f (1)$
(c) $f^{- 1} (0)$
(d) $f^{- 1} (- 1)$

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.

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Use the graph of y=f(x)given in Problem 44to evaluatethe following:(a)f(2)(b) f(1)(c) f-1(0)(d) f-1(-1)

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

Logic and Functions

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the graph of $y = f (x)$ given in Problem $44$ to evaluate
the following:
(a) $f (2)$
(b) $f (1)$
(c) $f^{- 1} (0)$
(d) $f^{- 1} (- 1)$