To find the zero of the function [tex]\( f(x) = 3 \sqrt{x+3} - 6 \)[/tex], we need to determine the value of [tex]\( x \)[/tex] that makes [tex]\( f(x) = 0 \)[/tex]. Here are the step-by-step calculations:
1. Set the function equal to zero:
[tex]\[
3 \sqrt{x+3} - 6 = 0
\][/tex]
2. Isolate the square root expression by adding 6 to both sides of the equation:
[tex]\[
3 \sqrt{x+3} = 6
\][/tex]
3. Divide both sides by 3 to solve for the square root term:
[tex]\[
\sqrt{x+3} = 2
\][/tex]
4. Square both sides of the equation to eliminate the square root:
[tex]\[
(\sqrt{x+3})^2 = 2^2
\][/tex]
[tex]\[
x + 3 = 4
\][/tex]
5. Subtract 3 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 4 - 3
\][/tex]
[tex]\[
x = 1
\][/tex]
Thus, the zero of the function [tex]\( f(x) = 3 \sqrt{x+3} - 6 \)[/tex] is [tex]\( x = 1 \)[/tex].
Among the given choices, the correct answer is:
D. [tex]\( x = 1 \)[/tex]
