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

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

a) State the domain of $\displaystyle f \cdot g$ and $\displaystyle \frac {f}{g}$
b) State a defining equation of $\displaystyle f \cdot g$ and $\displaystyle \frac {f}{g}$
c) Why are the domains of $\displaystyle f \cdot g$ and $\displaystyle \frac {f}{g}$ 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 = {$\displaystyle (x, y) |x\in \mathbb{R}, y = x^2 - 7x$}

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

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

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

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

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

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