# Thread: Product and Quotient of Functions

1. ## Product and Quotient of Functions

I don't know how to start this problem...because I don't understand the given sets...

Given:

f = { $(x, y) \epsilon R X R | y = x^2 - 7x$}

g = { $(x, y) \epsilon R X R | y = x$}

a) State the domain of $f \cdot g$ and $\frac {f}{g}$
b) State a defining equation of $f \cdot g$ and $\frac {f}{g}$
c) Why are the domains of $f \cdot g$ and $\frac {f}{g}$ different?

2. Originally Posted by Macleef
I don't know how to start this problem...because I don't understand the given sets...

Given:

f = { $(x, y) |x\in \mathbb{R}, y = x^2 - 7x$}

g = { $(x, y) | x\in \mathbb{R}, y = x$}
a) State the domain of $f \cdot g$ and $\frac {f}{g}$

The domain of $f\cdot g$ is the intersection of the domain of $f$ and $g$ which is still $\mathbb{R}$

The domain of $f/g$ is the intersection of the domain of $f$ and $g$ and $g\not = 0$ thus it is $\mathbb{R} \setminus \{ 0 \}$
b) State a defining equation of $f \cdot g$ and $\frac {f}{g}$
$f\cdot g = \{ (x,y)|x\in \mathbb{R}, y = x(x^2-7x)\}$
$f/g = \{(x,y)| x\in \mathbb{R} \setminus \{ 0 \}, y = (x^2-7x)/x=x-7\}$

3. Originally Posted by ThePerfectHacker
The domain of $f\cdot g$ is the intersection of the domain of $f$ and $g$ which is still $\mathbb{R}$

The domain of $f/g$ is the intersection of the domain of $f$ and $g$ and $g\not = 0$ thus it is $\mathbb{R} \setminus \{ 0 \}$

$f\cdot g = \{ (x,y)|x\in \mathbb{R}, y = x(x^2-7x)\}$
$f/g = \{(x,y)| x\in \mathbb{R} \setminus \{ 0 \}, y = (x^2-7x)/x=x-7\}$
For a, do you mean the domain is { $x^2 - 7x, 7x$} for f $\cdot$ g?
and for $\frac {f}{g}$, the domain is what?