Question

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

x=1
x=-1
x=9
x=-3

Answer 1

x = 1

Explanation:

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

Answer 2

x=1

Explanation:

Given function,

`f(x)=3√(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√(x+3)-6=0`

`3√(x+3)=6` ( Adding 6 on both sides )

`√(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.