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What is the zero of the function below?

[tex]\[ f(x) = 3 \sqrt{x+3} - 6 \][/tex]

A. [tex]\( x = -1 \)[/tex]

B. [tex]\( x = -3 \)[/tex]

C. [tex]\( x = 9 \)[/tex]

D. [tex]\( x = 1 \)[/tex]


Sagot :

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]