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leonid [27]
2 years ago
8

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

Mathematics
1 answer:
Lisa [10]2 years ago
7 0

Answer:

+1 and -1

Step-by-step explanation:

The function in this problem is:

f(x)=\frac{(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)\neq 0

which means:

x\neq 4\\x\neq -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.

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