x = 1
Step-by-step explanation:
Given data: [tex]f(x)=3 \sqrt{x+3}-6[/tex]
Recall: If f(x) = 0, then x is called the zero of the function.
To find zero of the function, take f(x) = 0.
[tex]\Rightarrow 3 \sqrt{x+3}-6=0[/tex]
Add 6 to both sides of the equation.
[tex]\Rightarrow 3 \sqrt{x+3}=6[/tex]
Divide both sides of the equation by 3.
[tex]\Rightarrow \sqrt{x+3}=2[/tex]
Taking square on both sides of the equation.
[tex]\Rightarrow(x+3)=2^{2}[/tex]
⇒ x + 3 = 4
⇒ x = 1
Hence, the zero of the function is 1.
