Question

Find the domain of the rational expression.

f(x) = -3/x^2-2x-35

Answer 1

`\\ \tt{:}\dashrightarrow y=(-3)/(x^2-2x-35)`

• To get the function undefined make denominator zero

`\\ \tt{:}\dashrightarrow x^2-2x-35=0`

`\\ \tt{:}\dashrightarrow x^2-7x+5x-35=0`

`\\ \tt{:}\dashrightarrow (x+5)(x-7)=0`

`\\ \tt{:}\dashrightarrow x=-5,7`

Domain is

`\\ \tt{:}\dashrightarrow R-\left\{-5,7\right\}`

Answer 2

all real numbers except -5 and 7

Explanation:

The function ...

f(x) = -3/(x^2-2x-35) = -3/((x+5)(x -7))

is undefined where the denominator is zero. The values of x that make the denominator zero are -5 and +7, so the domain is all real numbers except those.