# The value of f ( g ( 2 ) ) from the graphs of f and g . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.3, Problem 51E

(a)

To determine

## To evaluate: The value of f(g(2)) from the graphs of f and g.

Expert Solution

The value of f(g(2))=4 .

### Explanation of Solution

From the graph g, the value of g(2) is 5.

Thus, f(g(2))=f(5) .

From the graph f, it is identified that the value of f(5) is 4.

Therefore, the value of f(g(2))=4 .

(b)

To determine

### To evaluate: The value of g(f(0)) from the graphs of f and g.

Expert Solution

The value of g(f(0))=3 .

### Explanation of Solution

From the graph f, the value of f(0) is 0.

Thus, g(f(0))=g(0) .

From the graph g, it is identified that the value of g(0) is 3.

Therefore, the value of g(f(0))=3 .

(c)

To determine

### To find: The value of (f∘g)(0) from the graphs of f and g.

Expert Solution

The value of (fg)(0)=0 .

### Explanation of Solution

The composition function (fg)(0) is defined as f(g(0)) .

From the graph g, the value of g(0) is 3.

Thus, f(g(0))=f(3) .

From the graph f, it is identified that the value of f(3) is 0.

Therefore, the value of (fg)(0)=0 .

(d)

To determine

### To find: The value of (g∘f)(6) from the graphs of f and g.

Expert Solution

The value of (gf)(6)=undefined .

### Explanation of Solution

The composition function (gf)(6) is defined as g(f(6)) .

From the graph f, the value of f(6) is 6.

Thus, g(f(6))=g(6) .

Since the graph g is defined on the closed interval [−4, 4], the value of g(6) is undefined.

Therefore, the value of (gf)(6)=undefined .

(e)

To determine

### To find: The value of (g∘g)(−2) from the graphs of f and g.

Expert Solution

The value of (gg)(2)=4 .

### Explanation of Solution

The composition function (gg)(2) is defined as g(g(2)) .

From the graph g, the value of g(2) is 1.

Thus, (gg)(2)=g(1) .

Again from the graph g, it is identified that the value of g(1) is 4.

Therefore, the value of (gg)(2)=4 .

(f)

To determine

### To find: The value of (f∘f)(4) from the graphs of f and g.

Expert Solution

The value of (ff)(4)=2 .

### Explanation of Solution

The composition function (ff)(4) is defined as f(f(4)) .

From the graph f, the value of f(4) is 2.

Thus, f(f(4))=f(2) .

From the graph f, it is identified that the value of f(2) is −2.

Therefore, the value of (ff)(4)=2 .

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