b) Given functions $$ \mathrm{f}(\mathrm{x})=\sqrt{\mathrm{x}+4} $$ and $$ \mathrm{g}(\mathrm{x})=8 \mathrm{x}-8 $$. Find (f $$ \circ \mathrm{g})(\mathrm{x}) $$.

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UpStudy AI · Accepted Answer

1. Start with the composition $$(f \circ g)(x) = f(g(x))$$.

2. Substitute $$ g(x) = 8x - 8 $$ into $$ f(x) $$:
   $$
   f(g(x)) = \sqrt{(8x-8) + 4}.
   $$

3. Simplify the expression inside the square root:
   $$
   (8x-8) + 4 = 8x - 4.
   $$

4. Therefore, the composition becomes:
   $$
   (f \circ g)(x) = \sqrt{8x - 4}.
   $$

5. Optionally, factor inside the square root:
   $$
   \sqrt{8x-4} = \sqrt{4(2x-1)} = 2\sqrt{2x-1}.
   $$

The final answer is:
$$
(f \circ g)(x) = 2\sqrt{2x-1}.
$$
$$(f \circ g)(x) = 2\sqrt{2x - 1}$$.

b) Given functions \( \mathrm{f}(\mathrm{x})=\sqrt{\mathrm{x}+4} \) and \( \mathrm{g}(\mathrm{x})=8 \mathrm{x}-8 \). Find (f \( \circ \mathrm{g})(\mathrm{x}) \).

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