Question

What are the discontinuity and zero of the function f(x) = x^2 + 8x + 7 / x + 1

Answer 1

Discontinuity:

`x = - 1`

Zero:

`x = - 7`

EXPLANATION

The given rational function is

`f(x) = \frac{ {x}^(2) + 8x + 7 }{x + 1}`

We factor function to obtain:

`f(x) = ((x + 1)(x + 7))/(x + 1)`

This function is not continuous when

`(x + 1) = 0`

The function is not continuous at

`x = - 1`

When we simplify the function, we get;

`f(x) = x + 7`

The zero(s) occur at

`x + 7 = 0`

`x = - 7`

Answer 2

- Discontinuity at (-1,6)

- The zero is at (-7,0)

Explanation:

Given the function
`f(x)=(x^2 + 8x + 7)/(x+1)`, you need to factor the numerator. Find two number whose sum be 8 and whose product be 7. These are 1 and 7, then:

`f(x)=((x+1)(x+7))/((x+1))`

Then, the denominator is zero when
`x=-1`

Therefore,
`x=-1` does not belong to the Domain of the function. Then, (-1,6) is a discontinuity point.

Simplifying, you get:

`f(x)=x+7`

You can observe that a linear function is obtained.

This function is equal to zero when
`x=-7`, therefore the zero of the function is at (-7,0).