# The rule of function f ∘ g and the rule of the function g ∘ f 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 3E
To determine

## To fill: The rule of function f∘g and the rule of the function g∘f if the rule of the function f is add one and the rule of the function g is multiply by 2.

Expert Solution

If the rule of the function f is add one and the rule of the function g is multiply by 2, then the rule of fg is multiply by 2 and then add one, and the rule of gf is add one and then multiply by 2.

### Explanation of Solution

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))

If the rule of the function f is add one and the rule of the function g is multiply by 2, so for fg first apply the rule of function g, which is multiply by 2 and then apply the rule of function f, which is add one. The rule of fg is multiply by 2 and then add one.

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))

If the rule of the function f is add one and the rule of the function g is multiply by 2, so for gf first apply the rule of function f, which is add one and then apply the rule of function g which is multiply by 2. The rule of fg is add one and then multiply by 2.

Thus, if the rule of the function f is add one and the rule of the function g is multiply by 2, then the rule of fg is multiply by 2 and then add one, and the rule of gf is add one and then multiply by 2.

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