Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Manipulating Radical Functions

Manipulating Radical Functions 1.11 - Solution

arrow_back Return to Manipulating Radical Functions

Given that f(x)=2x3f(x)=\sqrt[3]{2x} and g(x)=-112x3,g(x)=\text{-}11\sqrt[3]{2x}, we will define (f+g)(x)(f+g)(x) and (fg)(x).(f-g)(x). Let's begin with the sum of the functions.

Adding Two Functions

Note that (f+g)(x)=f(x)+g(x).(f+g)(x)=f(x)+g(x). From here, we will substitute the given function rules and find the sum.
f(x)+g(x)f(x)+g(x)
2x3+(-112x3){\color{#0000FF}{\sqrt[3]{2x}}}+({\color{#009600}{\text{-}11\sqrt[3]{2x}}})
2x3112x3\sqrt[3]{2x}-11\sqrt[3]{2x}
(111)2x3(1-11)\sqrt[3]{2x}
-102x3\text{-}10\sqrt[3]{2x}

Subtracting Two Functions

Note that (fg)(x)=f(x)g(x),(f-g)(x)=f(x)-g(x), so we can proceed in the same way as we add two functions.
f(x)g(x)f(x)-g(x)
2x3(-112x3){\color{#0000FF}{\sqrt[3]{2x}}}-({\color{#009600}{\text{-}11\sqrt[3]{2x}}})
2x3+112x3\sqrt[3]{2x}+11\sqrt[3]{2x}
(1+11)2x3(1+11)\sqrt[3]{2x}
122x312\sqrt[3]{2x}