- 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)

- jamiebookeater

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- anonymous

replace x in the equation above with (a+b)

- anonymous

f(a+b)=3(a+b)+2 -4/(a+b)

- 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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## More answers

- 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

whats a+b tho

- anonymous

what do i do when i set it up like that

- xapproachesinfinity

that's what they asked you the evaluate
a+b standards as some variable

- xapproachesinfinity

hmm you can simply more if they ask you
just depends on the question

- xapproachesinfinity

in this case i would just leave it that way

- anonymous

what about the second one?

- 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

let me see if you can do g(a)

- anonymous

i thought were supposed to use the equation they gave us tho

- anonymous

i dont know

- xapproachesinfinity

what equation?

- anonymous

the second part

- xapproachesinfinity

you have g(x) right
find g(a) by replacing x with a

- 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

try to do g(a) first
let me see you do it

- anonymous

so 2-3(a)?

- xapproachesinfinity

yes g(a)=2-3a
what about g(a-b) now

- xapproachesinfinity

use the same function g(x)=2-3x
to find that

- anonymous

2-3(a-b)?

- xapproachesinfinity

yes good

- xapproachesinfinity

now f(a)

- anonymous

2-3(a)-2-3(a-b)+3(a)+2-4/(a)?

- xapproachesinfinity

that the next step let's not skip
do f(a) first

- xapproachesinfinity

i mean you have the idea but that's wrong because of the sign

- anonymous

3(a)+2-4/(a)

- xapproachesinfinity

yes
now g(a)-g(a-b)-f(a)=2-3a-(2-3(a-b))+3a+2-4/a

- 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

if ignored that it would be wrong
because the sign has to be distribute to 2-3(a-b)

- xapproachesinfinity

so no what we do it open up the parenthesis
2-3a-2+3(a-b)+3a+2-4/a

- xapproachesinfinity

we simplify more
=2-3a-2+3a-3b+3a+2-4/a
=....?

- xapproachesinfinity

finish it up

- anonymous

oh okay, thanks so much!!

- xapproachesinfinity

welcome!

- anonymous

so is the final answer 3a-3b+2-4/a

- xapproachesinfinity

yeah seems good!

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