help!!

**lovelygirlXx** · January 8th 2009, 03:28 PM

i need help on these questions plzz..
i need to find the domain of fg and f/g:
f(x)=x+2 g(x)=1/x+2

f(x)=3x^2+x^4+2 g(x)=4x-3

nd thanx !!=D

**Jhevon** · January 8th 2009, 03:36 PM

Originally Posted by lovelygirlXx

i need help on these questions plzz..
i need to find the domain of fg and f/g:
f(x)=x+2 g(x)=1/x+2

f(x)=3x^2+x^4+2 g(x)=4x-3

nd thanx !!=D

the domain is the set of all x-values for which the function is defined. basically, you need to find out what x-values "work" in these formulas.

example, for $f(x) = x + 2$ and $g(x) = \frac 1{x + 2}$

the domain of $f$ is $\text{dom}(f) = (-\infty, \infty)$ , that is, all real numbers. since you can plug in any real number $x$ into $x + 2$ and it will work, since it is a polynomial

for $g$ , the domain of $g(x)$ is $\text{dom}(g) = (-\infty, -2) \cup (-2, \infty)$ , that is, all real numbers except -2. why not -2? our function does not "work" there, because if x = -2, then we have a fraction in which the denominator is zero. dividing by zero is a no-no (see the pic)

now, find fg and f/g (do you know how?) and do the same analysis to come up with their domains. note, anything that is not in the domain of f and/or g, will not be in the domain of fg nor f/g

(i wrote the domains using interval notation. there are several ways you can write them...)

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