Answer:
6. [tex] (f - g)(x) = 2\sqrt[3]{5x} [/tex]
7. [tex] (f - g)(x) = 15\sqrt[4]{x-1} [/tex]
Step-by-step explanation:
To find [tex] (f - g)(x) [/tex], we subtract [tex] g(x) [/tex] from [tex] f(x) [/tex].
6)
Given:
- [tex] f(x) = - \sqrt[3]{5x} [/tex]
- [tex] g(x) = - 3\sqrt[3]{5x} [/tex]
We perform [tex] (f - g)(x) [/tex] as follows:
[tex] (f - g)(x) = f(x) - g(x) [/tex]
[tex] (f - g)(x) = (- \sqrt[3]{5x}) - (-3\sqrt[3]{5x}) [/tex]
[tex] (f - g)(x) = - \sqrt[3]{5x} + 3\sqrt[3]{5x} [/tex]
To combine these terms, notice that they share the same radical term. So we can factor out [tex] \sqrt[3]{5x} [/tex]:
[tex] (f - g)(x) = (-1 + 3)\sqrt[3]{5x} [/tex]
[tex] (f - g)(x) = 2\sqrt[3]{5x} [/tex]
So, [tex] (f - g)(x) = 2\sqrt[3]{5x} [/tex].
7)
Given:
[tex] f(x) = 12\sqrt[4]{x-1} [/tex]
[tex] g(x) = - 3\sqrt[4]{x-1} [/tex]
We find [tex] (f - g)(x) [/tex] as follows:
[tex] (f - g)(x) = f(x) - g(x) [/tex]
[tex] (f - g)(x) = (12\sqrt[4]{x-1}) - (- 3\sqrt[4]{x-1}) [/tex]
[tex] (f - g)(x) = 12\sqrt[4]{x-1} + 3\sqrt[4]{x-1} [/tex]
[tex] (f - g)(x) = (12+3)\sqrt[4]{x-1} [/tex]
[tex] (f - g)(x) = 15\sqrt[4]{x-1} [/tex]
So, [tex] (f - g)(x) = 15\sqrt[4]{x-1} [/tex].
