Question

given $f(x) = 8x - 8$ and $g(x) = sqrt{x + 4}$, find $(g circ f)(x)$. select a single answer $2sqrt{2x - 1}$ $8sqrt{x - 4}$ $2sqrt{2x + 1}$ $8sqrt{x + 4} - 8$

Explanation:

Step1: Define composite function

$(g \circ f)(x) = g(f(x))$

Step2: Substitute $f(x)$ into $g$

$g(8x - 8) = \sqrt{(8x - 8) + 4}$

Step3: Simplify the radicand

$\sqrt{8x - 4} = \sqrt{4(2x - 1)}$

Step4: Simplify the square root

$\sqrt{4} \cdot \sqrt{2x - 1} = 2\sqrt{2x - 1}$

Answer:

$2\sqrt{2x - 1}$