Question

Will give Medal and Fan. f(x)=(x^2+3x-4) and g(x)=(x+4). what is f*g and it's domain.
What is f/g and it's domain.

Answer 1

@ganeshie8

Answer 2

@campbell_st

Answer 3

@uri

Answer 4

well if you write it out\[\frac{f(x)}{g(x)} = \frac{(x^2 + 3x -4)}{x - 4}\]

you might like to factor the numerator.... and see if there are common factors.

Answer 5

Well the g(x)=x+4

Answer 6

opps yes the denominator should be (x + 4)

Answer 7

So I can remove one x correct?

Answer 8

no... factor the numerator..... can you do that...?

Answer 9

Well, -3 and -1

Answer 10

I suck at anything to do with factoring, so Helping me with this first part will be the hardest part I promise lol.

Answer 11

not quite... find the factors of -4 that add to 3.... the larger factor is positive and the smaller factor is negative.

Answer 12

so 4 and -1, yeah. I did it the opposit way and found things that add to -4 and multiply to 3.

Answer 13

so the numerator is (x + 4)(x -1)

is there a common factor...?

Answer 14

4...?

Answer 15

well the common factor is (x + 4)

which means f/g = (x - 1)

so there are 2 options... the simplified verion has a domain of all real x.

of if you look at the original problem x cannont be -4 as this gives a zero denominator.

the point x = -4 in this case is a point of discontinuity

so it depends on the level of math you are doing....

choices, all real x or all real x except x = -4

Answer 16

Okay. I understand, after the factoring incident lol. All real x except x=-4 is what i was looking for. Thank you.