## zeesbrat3 one year ago For f of x equals the quotient of the quantity 1 minus x and the quantity 1 plus x and g of x equals the quotient of the quantity x and the quantity 1 minus x, find the simplified form for f [g(x)] and state the domain.

1. zeesbrat3

@Hero @nincompoop @abb0t @kropot72 @Whitemonsterbunny17 @freckles @Miracrown @vera_ewing

2. zeesbrat3

@ganeshie8

3. zeesbrat3

hey

4. ganeshie8

$f(x)=\dfrac{1-x}{1+x}$ $g(x)=\dfrac{x}{1-x}$ like this ?

5. zeesbrat3

Yes

6. zeesbrat3

$\frac{ 1- \frac{ x }{ 1-x } }{ 1 + \frac{ x }{ 1-x } }$

7. ganeshie8

looks good, multply $$1-x$$ top and bottom

8. ganeshie8

$\frac{ 1- \frac{ x }{ 1-x } }{ 1 + \frac{ x }{ 1-x } }= \frac{ \left(1- \frac{ x }{ 1-x }\right)\left(1-x\right) }{ \left(1 + \frac{ x }{ 1-x }\right)\left(1-x\right) } = \dfrac{1-x-x}{1-x+x}=1-2x$

9. zeesbrat3

why does it seem so much harder?

10. ganeshie8

it is not hard if you simply follow the rules

11. zeesbrat3

i see what i did wrong though

12. zeesbrat3

i multiplied the entire fraction off the bottom, not just the denominator

13. ganeshie8

For domain part, notice that $$g(x)=\dfrac{x}{1-x}$$ is undefined at $$x=1$$ and since $$1-2x$$ is defined for all real numbers, the domain of $$f(g(x))=1-2x$$ is all real number except $$1$$

14. zeesbrat3

Thank you

15. zeesbrat3

Can you help with a few more? @ganeshie8

16. zeesbrat3

A particle moves on a line away from its initial position so that after t hours it is s = 2t2 +3t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.