1. ## Help with composites please!

Here's the question:

Find the composites for the relations defined.

R1={(x,y) member of real numbers x real numbers: y=x}
R2={(x,y) member of real numbers x real numbers: y=-5x+2}

a) R1compositeR1
b)R2compositeR2

a) I was thinking that R1compositeR1={(x,y) member of real numbers x real numbers: x=y}=R1
b) I'm not to sure how to do and thats the one I need help on.

Thank you!!

2. let
$\displaystyle f(x)=x$ and $\displaystyle g(x)=-5x+2$

Then

$\displaystyle (f \circ g)(x)=g(x)=-5x+2$ and

$\displaystyle (g \circ f)(x)=-5f(x)+2=-5x+2$

Since both f and g are defined on all of R and both map onto R

The domain and Range are all real numbers.

I hope this helps
good luck.

3. Originally Posted by TheEmptySet
let
$\displaystyle f(x)=x$ and $\displaystyle g(x)=-5x+2$

Then

$\displaystyle (f \circ g)(x)=g(x)=-5x+2$ and

$\displaystyle (g \circ f)(x)=-5f(x)+2=-5x+2$

Since both f and g are defined on all of R and both map onto R

The domain and Range are all real numbers.

I hope this helps
good luck.
I still don't understand. Does this mean that R2compositeR2={(x,y) member of real numbers x real numbers: y=-5x+2}=R2?

4. Originally Posted by calcprincess88
I still don't understand. Does this mean that R2compositeR2={(x,y) member of real numbers x real numbers: y=-5x+2}=R2?
R1 and R2 are just fuctions.

R1=$\displaystyle f(x)=x$

R2=$\displaystyle g(x)=-5x+2$

I just called R1 f and R2 g

$\displaystyle R2 \circ R2 = g(x) \circ g(x)=g(g(x))=-5g(x)+2=-5(-5x+2)+2=25x-8$

and

$\displaystyle R1 \circ R1 = f(x) \circ f(x)=f(f(x))=f(x)=x$

5. ohhhh I get it. I'm sorry. I didn't understand at first what you were saying but now I do! Thank you soooo much for your patience and help!! I really appreciate it!!!