Question

What are the zeros of

f(x)=
`(x)/(9x^(2) -4)`

will give branniest, please show work and solve algebraically

Answer 1

First, we need to find the domain of the function.

We can not divide by zero, therefore:

`9x^2-4\\eq0\ \ \ \ |\text{add 4 to both sides}\\\\9x^2\\eq4\ \ \ \ |\text{divide both sides by 9}\\\\x^2\\eq(4)/(9)\ \ \ \ \ |\text{square root both sides}\\\\x\\eq\pm\sqrt{(4)/(9)}\\\\x\\eq-(2)/(3)\ \wedge\ x\\eq(2)/(3)`

The zeros of function are x-s, for which f(x) = 0:

`f(x)=(x)/(9x^2-4)\\\\f(x)=0\Rightarrow(x)/(9x^2-4)=0`

The fraction is zero if the numerator is equal to zero. Therefore:

`f(x)=0\iff x=0\in D`

Answer 2

A zero of a function is a value of the independent variable (here, that's x) at which the function is zero. In this particular case, the only 'zero' is 0.