Question

What are the zeros of the function f(x) = x^2 + 2x- 8 / x^2 - 2x - 8

Answer 1

Answer:

x=-4 and x=2

Step-by-step explanation:

You are given the function

$f(x)=\dfrac{x^2+2x-8}{x^2-2x-8}$

The zeros of the function are those value of x, for which $f(x)=0$

First, find x for which function is undefined

$x^2-2x-8\neq0\\ \\x^2-4x+2x-8\neq 0\\ \\x(x-4)+2(x-4)\neq 0\\ \\(x-4)(x+2)\neq 0\\ \\x\neq 4\text{ and }x\neq -2$

Now find points at which f(x)=0:

$f(x)=0\Rightarrow x^2+2x-8=0\\ \\x^2+4x-2x-8=0\\ \\x(x+4)-2(x+4)=0\\ \\(x-2)(x+4)=0\\ \\x=2\text{ or }x=-4$

For both these values (x=-4 and x=2) function f(x) is defined, then x=-4 and x=2 are zeros of the function.

Answer 2

Answer:

(-4,2) ape x people

Step-by-step explanation: