# Find the value of f o g for given two functions f ( x ) = 1 + x 2 and g ( x ) = x − 1 . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 76RE

a.

To determine

## Find the value of fog for given two functions f(x)=1+x2 and g(x)=x−1 .

Expert Solution

The value of fog(x)=x

### Explanation of Solution

Given: The given two functions f(x)=1+x2 and g(x)=x1 .

The objective is to find the value of fog

(fog)=f(g(x))=f(x1)=1+(x1)=1+x1=x

Hence, the value of fog(x)=x

b.

To determine

### Find the value of gof for given two functions f(x)=1+x2 and g(x)=x−1 .

Expert Solution

The value of gof(x)=x

### Explanation of Solution

Given: The given two functions f(x)=1+x2 and g(x)=x1 .

The objective is to find the value of gof

(g 0f)=g(f(x))=g(1+x2)=(1+x21)=x2=x

Hence, the value of gof(x)=x

c.

To determine

### Find the value of fog(2) for given two functions f(x)=1+x2 and g(x)=x−1 .

Expert Solution

The value of fog(2)=2

### Explanation of Solution

Given: The given two functions f(x)=1+x2 and g(x)=x1

The objective is to find the value of

fog(2)

now,

(fog)(2)=f(g(2))=f(21)=f(1)=2

Hence, the value of fog(2)=2

d.

To determine

### Find the value of fof=(2) for given two functions f(x)=1+x2 and g(x)=x−1

Expert Solution

The value of fof(2)=26

### Explanation of Solution

The objective is to find the value of

fof=(2)

now,

(fof)(2)=f(f(2))=f(1+22)=f(5)=26

Hence, the value of fof(2)=26

e.

To determine

### Find the value of fogof for given two functions f(x)=1+x2 and g(x)=x−1

Expert Solution

The value of fogof=1+x2

### Explanation of Solution

The objective is to find the value of

fogof

now,

(fogof)(x)=fog(f(x))=fog(1+x2)=f(1+x21)=f(x2)f(x2)=1+(x2)2=1+x2

Hence, the value of fogof=1+x2

f.

To determine

### Find the value of gofog for given two functions f(x)=1+x2 and g(x)=x−1

Expert Solution

The value of gofog=x1 .

### Explanation of Solution

Given:

The objective is to find the value of

gofog

Now,

(gofog)(x)=gof(g(x))=gof(x1)=g(1+(x1)2)=g(1+x1)g(x)=x1

Hence, the value of gofog=x1 .

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