Find domain?

Question

f(x)= 3x / (x^2 + 5x + 4)

Answer 1

the only restriction here is that the denominator can not equal 0.
therefore:
x^2+5x+4=0
x^2+x+4x+4=0
x(x+1)+4(x+1)=0
(x+1)(x+4)=0
x=-1 ; x=-4.
the domain is: all real numbers except :-1 ;-4.

Answer 2

Domain is a way of saying, "What values can x be?"

In a fraction, the only restriction is that the bottom does NOT equal 0. Therefore, we try and see what happens when we make it 0, so we can state our domain regarding what our x values are NOT.

Let's equate the denominator to 0.

x^2 + 5x + 4 = 0

Factoring, we get

(x + 4) (x + 1) = 0

And then solving, we get x = -1, -4

So our domain is all real numbers that excludes -1 and -4, OR

(-infinity, -4) U (-4, -1) U (-1, infinity)

The round brackets represent the exclusion of the value next to it. Infinity ALWAYS has round brackets.

Answer 3

The only restriction here is that the denominator can not equal zero. Therefore:

(x+5)(X-4)=0 yields x=-5 and x=4
Thus the domain is { all real numbers except -5 and 4

Answer 4

All rational values of x as below

minus infinity to -2
and 0 to plus infinity