Question

function help?

Answer 1

\[Find (\frac{ f }{ g }) (x) for the functions provided: f(x) = x^2 − 9, g(x) = 3 − x\]

Answer 2

@Michele_Laino

Answer 3

here we have to evaluate the subsequent ratio:
\[\frac{{{x^2} - 9}}{{3 - x}}\]

Answer 4

ok

Answer 5

i got x+3

Answer 6

now, we have to keep in mind that we can write the subsequent identity:
\[{x^2} - 9 = \left( {x - 3} \right)\left( {x + 3} \right)\]
so substituting in our ratio, we get:
\[\frac{{{x^2} - 9}}{{3 - x}} = \frac{{\left( {x - 3} \right)\left( {x + 3} \right)}}{{ - \left( {x - 3} \right)}}\]
since we have:
3-x=-(x-3)
Please simplify, what do you get?

Answer 7

either x+3 or -x-3

Answer 8

oops i think im wrong

Answer 9

you can cancel similar terms

Answer 10

hint:

Answer 11

oh i totally see it now

Answer 12

so, what is the result?

Answer 13

-x-3?

Answer 14

oh duh its x+3 because the others cancel out

Answer 15

there is -1 at the denominator

Answer 16

hint:

Answer 17

at the numerator I have simplified by (x-3), namely I have computed this ratio:
\[\frac{{\left( {x - 3} \right)}}{{\left( {x - 3} \right)}} = 1\]
whereas at the denominator I have simplified by (x-3) too, so I have computed this ratio:
\[\frac{{\left( {x - 3} \right)}}{{ - \left( {x - 3} \right)}} = - 1\]

Answer 18

ok

Answer 19

i still got -x-3 xD

Answer 20

that's right!
-x-3= - (x+3)

Answer 21

so its f/g (x)= -x-3?

Answer 22

yes!

Answer 23

Yay! thanks again. P.s I really want to visit Italy :)

Answer 24

thanks! :)

Answer 25

and I really want to visit The United States of America! :)

Answer 26

ive heard that the food over there is amazing xD and p.s the american food is kind of gross. lol