Question

What are the zeros of the function below? F(x)= (x-1)(x+1)/6(x-4)(x+7)

Answer 1

+1 and -1

Explanation:

The function in this problem is:

`f(x)=((x-1)(x+1))/(6(x-4)(x+7))`

First of all, we have to define the domain of the function, which is the set of values of x for which the function is defined.

In order to find the domain, we have to require that the denominator is different from zero, so

`6(x-4)(x+7)\\eq 0`

which means:

`x\\eq 4\\x\\eq -7`

So the domain is all values of x, except from 4 and -7.

Now we can solve the problem and find the zeros of the function. The zeros can be found by requiring that the numerator is equal to zero, so:

`(x-1)(x+1)=0`

This is verified if either one of the two factors is equal to zero, therefore:

`x-1=0\\\rightarrow x=+1`

and

`x+1 = 0\\\rightarrow x=-1`

We see that both values are part of the domain, so they are acceptable values: so the zeros of the function are +1 and -1.