# The values of functions f ( x ) , g ( x ) , ( f ∘ g ) ( x ) and ( g ∘ f ) ( x ) if the rule of the function f is add one and the rule of the function g is multiply by 2.

### 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 2.6, Problem 4E
To determine

## To evaluate: The values of functions f(x) , g(x) , (f∘g)(x) and (g∘f)(x) if the rule of the function f is add one and the rule of the function g is multiply by 2.

Expert Solution

The values of function f(x) is g(x) is 2x , (fg)(x) is 2x+1 , (gf)(x) is 2(x+1) .

### Explanation of Solution

Section1:

The rule of the function f is adding one.

So, the value of function f(x) is added by one.

f(x)=x+1

Thus, the value of function f(x) is x+1 .

Section2:

The rule of the function f is multiply by 2.

So, the value of function g(x) is multiplied by one.

g(x)=2x

Thus, the value of function g(x) is 2x .

Section3:

The rule of the function f is add one and the rule of the function g is multiply by 2.

From section 2:

The value of function f(x) is x+1 .

From section3:

The value of function g(x) is 2x .

The function fg is called the compositions of functions f and g and the domain of fg is set of all x in the domain of g such that g(x) is in the domain of f, that means,

(fg)(x)=f(g(x))

Substitute the values of f(x) and g(x) in above formula,

(fg)(x)=f(2x)=2x+1

Thus, the value of function (fg)(x) is 2x+1 .

Section4:

The rule of the function f is add one and the rule of the function g is multiply by 2.

From section 2:

The value of function f(x) is x+1 .

From section3:

The value of function g(x) is 2x .

The function gf is called the compositions of functions g and f and the domain of gf is set of all x in the domain of f such that f(x) is in the domain of g, that means,

(gf)(x)=g(f(x))

Substitute the values of f(x) and g(x) in above formula,

(gf)(x)=g(x+1)=2(x+1)

Thus, the value of function (gf)(x) is 2(x+1) .

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