Question

Someone help pls asap

Answer 1

`→(g - f)(x) = g(x) - f(x) \\ → (log(x - 3) + 6) - (\sqrt[3]{12x + 1} + 4) \\→ log(x - 3) + 6 - \sqrt[3]{12x + 1} - 4 \\→\boxed{ log(x - 3) - \sqrt[3]{12x + 1} + 2}✓`

D. is the right answer.

Answer 2

`(g - f)(x) = log(x-3)- \sqrt[3]{12x +1} + 2`

Explanation:

Given

`f(x) = \sqrt[3]{12x +1} + 4`

`g(x) = log(x-3)+6`

Required

Determine (g - f)(x)

In functions:

`(g - f)(x) = g(x) - f(x)`

So, we have:

`(g - f)(x) = log(x-3)+6 - (\sqrt[3]{12x +1} + 4)`

Open bracket

`(g - f)(x) = log(x-3)+6 - \sqrt[3]{12x +1} - 4`

Collect Like Terms

`(g - f)(x) = log(x-3)- \sqrt[3]{12x +1} - 4+6`

`(g - f)(x) = log(x-3)- \sqrt[3]{12x +1} + 2`