Question

Let f(x) = (x^2 + 3x – 4) and g(x) = (x + 4).
a. Find f • g and state the domain.
b. Find f/g and state the domain.

Answer 1

So I know I start by multiplying (x^2+3x-4)(x+4)... I get x^3+7x^2+8x-16 what now?

Answer 2

f • g=x^3+4x^2+3x^2+12x-4x-16=x^3+7x^2+8x-16 the domain means what values can x get, here, x can be any real number. so the domain is all numbers.

Answer 3

How do I know it is all numbers and there isn't like one number that doesn't work? Is there a way to check that?

Answer 4

f/g=(x^2 + 3x – 4)/(x+4) as we know, the denominator can't be equal to 0, so x+4 can't be equal to 0, that means, x can be any number but -4

Answer 5

if there is a square root or a denominator, you must consider that denominator can't be 0 and the expression in the square root is >=0

Answer 6

Wait so what is f/g?

Answer 7

the domain of f/g is any real number but -4

Answer 8

Yeah, that's the domain, but it says find f/g and then it says also find the domain, I thought that that means I need two answers there?

Answer 9

f/g=(x^2 + 3x – 4)/(x+4)

Answer 10

wait, what would be the steps to find that the domain of f/g is all but -4?

Answer 11

is it like x+4>=0 then subtract 4 from both sides so you have x>=-4?

Answer 12

thanks!

Answer 13

now what @Hero