Question

composite radical functions can
$f(x) = 9\sqrt{x + 6}$
$g(x) = \sqrt3{x} - 1$
find $g(f(3))$.

Explanation:

Step1: Calculate $f(3)$

Substitute $x=3$ into $f(x)$:
$$f(3)=9\sqrt{3+6}$$
Simplify the expression inside the square root:
$$f(3)=9\sqrt{9}=9\times3=27$$

Step2: Calculate $g(f(3))$

Substitute $x=f(3)=27$ into $g(x)$:
$$g(27)=\sqrt[3]{27}-1$$
Simplify the cube root:
$$g(27)=3-1$$

Answer:

$2$