Pre calc review - interval notation

[datafiend]

Homework Statement

What's the domain of 14/x²-x-6, in interval notation?

Homework Equations

$\underline{14}$x²-x-6

The Attempt at a Solution

[3, + infinity)
[-2,- infinity)
Sorry, I can't find the infinity symbol

Thx

 

[Ray Vickson]

Homework Statement

What's the domain of 14/x²-x-6, in interval notation?

Homework Equations

$\underline{14}$x²-x-6

The Attempt at a Solution

[3, + infinity)
[-2,- infinity)
Sorry, I can't find the infinity symbol

Thx

You wrote
$$\frac{14}{x^2} -x-6$$
when read using standard rules for parsing mathematical expressions. Did you really mean that, or did you want
$$\frac{14}{x^2 - x - 6} \: ?$$
If you meant the latter you absolutely MUST use parentheses, like this: 14/(x^2 - x - 6).

 

[datafiend]

My mistake, the denominator SHOULD be in parentheses.

 

[LCKurtz]

Homework Statement

What's the domain of 14/(x²-x-6), in interval notation?

Homework Equations

$\frac{14}{x^2-x-6}$

The Attempt at a Solution

[3, + infinity)
[-2,- infinity)
Sorry, I can't find the infinity symbol

Thx

The Attempt at a Solution

What about values between 3 and -2?

 

[HallsofIvy]

Homework Statement

What's the domain of 14/x²-x-6, in interval notation?

You mean 14/(x²- x- 6)= 14/((x- 3)(x+ 2))

Homework Equations

$\underline{14}$x²-x-6

The Attempt at a Solution

[3, + infinity)

No, this is wrong because it does not include such numbers as x= 0 for which 14/(0- 0- 6)= -7/3 or x= -5 for which 14/(25+ 5- 6)= 7/12.

[-2,- infinity)

Strictly speaking this is bad notation- it should be (-infinity, -2]. (The smaller goes on the left.)
But even that is not correct because it does not contain x= 0 and x= 5 for which 14/(25- 5- 6)= 1.

The correct answer is NOT a single interval, it is a union of three disjoint intervals.

Sorry, I can't find the infinity symbol

Thx

Homework Statement

Homework Equations

The Attempt at a Solution

 

[skiller]

Strictly speaking this is bad notation- it should be (-infinity, -2]. (The smaller goes on the left.)
But even that is not correct because it does not contain x= 0 and x= 5

I'm surprised no one's mentioned the incorrect use of the square bracket to end the set.