BuyFind

Precalculus: Mathematics for Calcu...

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

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

Expert Solution

Answer to Problem 3E

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.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!