Question

someone help pls asap

Answer 1

Answer:

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

Step-by-step 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

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

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

Answer 2

Answer:

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

D. is the right answer.