Question

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)

Answer 1

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

Answer 2

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

Answer 3

wherever you x replace by a+b
\[f(x)=3x+2-\frac{4}{x}\]
\[f(\color {red}{a+b})=3(\color{red}{a+b})+2-\frac{4}{\color{red}{a+b}}\]

Answer 4

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

Answer 5

whats a+b tho

Answer 6

what do i do when i set it up like that

Answer 7

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

Answer 8

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

Answer 9

in this case i would just leave it that way

Answer 10

what about the second one?

Answer 11

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)

Answer 12

let me see if you can do g(a)

Answer 13

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

Answer 14

i dont know

Answer 15

what equation?

Answer 16

the second part

Answer 17

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

Answer 18

i broke it down to steps as you can see
first find g(a)
then g(a-b)
then f(a) all separately

Answer 19

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

Answer 20

so 2-3(a)?

Answer 21

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

Answer 22

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

Answer 23

2-3(a-b)?

Answer 24

yes good

Answer 25

now f(a)

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

finish it up

Answer 36

oh okay, thanks so much!!

Answer 37

welcome!

Answer 38

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

Answer 39

yeah seems good!