# To find the functions f o g , g o f , f o f , g o g and their domains of given f ( x ) = x and g ( x ) = 2 x − 4

### 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 78RE
To determine

## To find the functions fog , gof , fof , gog and their domains of given f(x)=x and g(x)=2x−4

Expert Solution

The function fog(x)=2x4 and    domain(4,)

The function gof(x)=2x4 and domain[0,],except x16

The function (fof)(x)=x4 and the domainis [0,]

The function gog(x)=x494x and the domain is all real numbers except for x in the set {92}

Range (,1)(1,)

### Explanation of Solution

The given functions are

f(x)=xg(x)=2x4

The domain of f is {x|x0} and the domain of g(x)={x/x4}

The intersection of the domain f and g is

{x/x0 and x4}=[0,4)(4,)

fog(x)=f(g(x))=f(2x4)=2x4    domain(4,)

gof(x)=g(f(x))=g(x)=2x4   domain[0,),exceptx16

(fof)(x)=f(f(x))=f(x)=x4 domain[0,)

gog(x)=g(g(x))=g(2x4)=22x44=224(x4)x4=224x+16x4=2184xx4=2(x4)184x=x494x

the domain is all real numbers except for x in the set {92}

Range (,1)(1,)

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