Question

f(x)=3x+12
a. determine the inverse of this function and name it g(x).
b. use composite functions to show that these functions are inverses.
c. evaluate f(g(-2)). Explain: what is the domain?

Answer 1

(I am putting y instead of f(x) so it is easier...)
is the inverse
x=3y+12
-3y=-x+12
y=1/3x-4
correct?

I'm not sure what to do for b....

Answer 2

looks good to me

Answer 3

okay

Answer 4

b. use composite functions to show that these functions are inverses.
put \(f(x)=3x+12,g(x)=\frac{1}{3}x-4\) then compute
\[g(f(x))\] and see that you get \(x\) as the final answer

Answer 5

so do I plug it in for x? I'm confused :(

Answer 6

do you know how to write a composite function?

Answer 7

sorta........but right now my brain is fried from too much math and homework that it isn't wanting to work....so
g(x)=1/3(3x+12)+4
correct?

Answer 8

\[g(f(x))=g(3x+12)=\frac{1}{3}(3x+12)-4\] yes, except you made a typo and had a \(+4\) at the end, it should be \(-4\)

Answer 9

then
g(x)=x+8
?

Answer 10

exactly because you made that mistake

Answer 11

whoopsies!

Answer 12

now you get just \(x\) right?

Answer 13

actually it is just g(x)=x then

Answer 14

yep

Answer 15

no dear, it is not \(g(x)=x\) it is \(g(f(x))=x\)

Answer 16

but that is probably what you meant

Answer 17

oh! okay

Answer 18

sorry.....my mistake :)

Answer 19

okay so what do I do next?

Answer 20

go have a beer?
oh no, still need
c. evaluate f(g(-2)). Explain: what is the domain

Answer 21

lol

Answer 22

\[f(g(-2))=-2\] because the functions are invereses

Answer 23

okay

Answer 24

i do not know what "explain what is the domain" means
it is not english

Answer 25

wait........I'm confused on how that is possible....sorry! lol

Answer 26

nor is it math

Answer 27

how is what possible?

Answer 28

oh never mind lol

Answer 29

well I just need to find the domain and explain how I get that....I think

Answer 30

you just proved that
\[g(f(x))=x\] for any \(x\) it has to be true for \(-2\) that
\[g(f(-2))=-2\]

Answer 31

the domain of a polynomial function is all real numbers unless you specify otherwise
in this case you have a line, so the range is all real numbers as well

Answer 32

okay thank you so much!!!!

Answer 33

yw