Question

What is the zero of the function below? f(x)=3 square root x+3 -6x=1x=-1x=9x=-3

Answer 1

Answer:

x=1

Step-by-step explanation:

Given function,

$f(x)=3\sqrt{x+3}-6$

Since, the zeroes of a function are those input values for which the function gives the output zero,

So, for the zeroes of f(x),

f(x) = 0

$\implies 3\sqrt{x+3}-6=0$

$3\sqrt{x+3}=6$      ( Adding 6 on both sides )

$\sqrt{x+3}=2$        ( Dividing both sides by 3 )

$x+3=4$                ( Taking square of both sides )

$x = 1$                   ( Subtracting 3 from both sides )

Hence, the zero of the given function is, x = 1.

First option is correct.

Answer 2

Answer:

x = 1

Step-by-step explanation:

$f(x)=3\sqrt{x+3}-6\\\\\text{Domain:}\ x+3\geq0\to x\geq-3\\\\\text{The zero}\to f(x)=0\\\\3\sqrt{x+3}-6=0\qquad\text{add 6 to both sides}\\\\3\sqrt{x+3}=6\qquad\text{divide both sides by 3}\\\\\sqrt{x+3}=2\iff x+3=2^2\\\\x+3=4\qquad\text{subtract 3 from both sides}\\\\x=1$