determine the domain for f(x)= x/(over) x^2-4

Question

campbell_st · Answer

well have a look at the values of x you can't put into the denominator, as they will create a value of zero, which is undefined in the denominator

so solve 

$$x^2 - 4 = 0$$

these will be the values that are excluded from the domain of all real x

anonymous · Answer

does it equal two

campbell_st · Answer

there are two values, one of them  is x =  2 whats the other...?

anonymous · Answer

the other is x=0?

anonymous · Answer

maybe, i'm not sure

anonymous · Answer

Factor

anonymous · Answer

x^2-4

campbell_st · Answer

nope can you factor 

$$x^2 - 4 = 0$$


its the difference of 2 squares

anonymous · Answer

$$\Huge x^2-a^2=(x+a)(x-a)$$

anonymous · Answer

i don't understand, the first one is x=2 but the other one  do i get by plugging in x^2-4 into that equation?

campbell_st · Answer

ok... what is the value of 

(-2)^2 =

anonymous · Answer

-4

campbell_st · Answer

well look at it this way 

what is 

$$-2 \times -2 = $$

anonymous · Answer

-4

campbell_st · Answer

multiplying 2 negatives gives a positive

so the answer is 4

anonymous · Answer

oh oopsy sorry

campbell_st · Answer

so the solutions to the quadratic 

$$x^2 - 4 = 0$$

is 

$$x = \pm 2$$

anonymous · Answer

Cause every number really has a positive and negative square root

campbell_st · Answer

so those values are excluded from the domain. 

so the domain of the function is all real x except -2 and 2

anonymous · Answer

oh, okay then. so its all the numbers except 2 and -2

anonymous · Answer

thank you