anonymous
  • anonymous
Given the functions f(x) = 3x + 2 −4/x and g(x) = 2 − 3x, find the indicated values. a) f(a + b) b) g(a) − g(a − b) + f(a)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
replace x in the equation above with (a+b)
anonymous
  • anonymous
f(a+b)=3(a+b)+2 -4/(a+b)
xapproachesinfinity
  • xapproachesinfinity
wherever you x replace by a+b \[f(x)=3x+2-\frac{4}{x}\] \[f(\color {red}{a+b})=3(\color{red}{a+b})+2-\frac{4}{\color{red}{a+b}}\]

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xapproachesinfinity
  • xapproachesinfinity
if for example f(x)=x^-2 they ask f(c) \[f(\color{blue}{c})=\color{blue}{c}^2-2\] just a matter of replacing the dummy variable
anonymous
  • anonymous
whats a+b tho
anonymous
  • anonymous
what do i do when i set it up like that
xapproachesinfinity
  • xapproachesinfinity
that's what they asked you the evaluate a+b standards as some variable
xapproachesinfinity
  • xapproachesinfinity
hmm you can simply more if they ask you just depends on the question
xapproachesinfinity
  • xapproachesinfinity
in this case i would just leave it that way
anonymous
  • anonymous
what about the second one?
xapproachesinfinity
  • xapproachesinfinity
second you gonna do each one separately g(a) g(a-b) f(a) after that the results do g(a)-g(a-b)+f(a)
xapproachesinfinity
  • xapproachesinfinity
let me see if you can do g(a)
anonymous
  • anonymous
i thought were supposed to use the equation they gave us tho
anonymous
  • anonymous
i dont know
xapproachesinfinity
  • xapproachesinfinity
what equation?
anonymous
  • anonymous
the second part
xapproachesinfinity
  • xapproachesinfinity
you have g(x) right find g(a) by replacing x with a
xapproachesinfinity
  • xapproachesinfinity
i broke it down to steps as you can see first find g(a) then g(a-b) then f(a) all separately
xapproachesinfinity
  • xapproachesinfinity
try to do g(a) first let me see you do it
anonymous
  • anonymous
so 2-3(a)?
xapproachesinfinity
  • xapproachesinfinity
yes g(a)=2-3a what about g(a-b) now
xapproachesinfinity
  • xapproachesinfinity
use the same function g(x)=2-3x to find that
anonymous
  • anonymous
2-3(a-b)?
xapproachesinfinity
  • xapproachesinfinity
yes good
xapproachesinfinity
  • xapproachesinfinity
now f(a)
anonymous
  • anonymous
2-3(a)-2-3(a-b)+3(a)+2-4/(a)?
xapproachesinfinity
  • xapproachesinfinity
that the next step let's not skip do f(a) first
xapproachesinfinity
  • xapproachesinfinity
i mean you have the idea but that's wrong because of the sign
anonymous
  • anonymous
3(a)+2-4/(a)
xapproachesinfinity
  • xapproachesinfinity
yes now g(a)-g(a-b)-f(a)=2-3a-(2-3(a-b))+3a+2-4/a
xapproachesinfinity
  • xapproachesinfinity
the difference btw what i just did and what you did is i put those parenthesise before 2-3(a-b) because of the sign that came before it
xapproachesinfinity
  • xapproachesinfinity
if ignored that it would be wrong because the sign has to be distribute to 2-3(a-b)
xapproachesinfinity
  • xapproachesinfinity
so no what we do it open up the parenthesis 2-3a-2+3(a-b)+3a+2-4/a
xapproachesinfinity
  • xapproachesinfinity
we simplify more =2-3a-2+3a-3b+3a+2-4/a =....?
xapproachesinfinity
  • xapproachesinfinity
finish it up
anonymous
  • anonymous
oh okay, thanks so much!!
xapproachesinfinity
  • xapproachesinfinity
welcome!
anonymous
  • anonymous
so is the final answer 3a-3b+2-4/a
xapproachesinfinity
  • xapproachesinfinity
yeah seems good!

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