Question

Let f(x) = x + 8 and g(x) = x2 – 6x – 7. Find f(g(2)).
:)))

Answer 1

do you know how to find
\[g(2)\]?

Answer 2

no clue, i read through this lesson and didn't understand a thing..

Answer 3

ok
\[g(x)=x^2-6x-7\] so
\[g(2)\] means replace x by 2

Answer 4

i.e. where you see "x" you put "2" and get a number, namely
\[g(2)=2^2-6\times 2-7\] good so far?

Answer 5

yes

Answer 6

so what do you get when you compute
\[g(2)\]?

Answer 7

2+8=10 and 2^2-12-7=2^2+5 i think?

Answer 8

oh sorry i confused you. we are ignoring
\[f(x)\] for the moment, and just concentrating on
\[g(x)\] and we need
\[g(2)\]

Answer 9

what you wrote is correct,
\[g(2)=2^2-12-7\] and this number is
\[4-12-7=-8-7=-15\] so
\[f(2)=-15\]

Answer 10

now we are not asked for
\[f(2)\] we are asked for
\[f(g(2))\] and we work from the inside out. we already have computed
\[g(2)=-15\] so
\[f(g(2))=f(-15)\]

Answer 11

btw you read "f of g of 2"

Answer 12

and
\[f(x)=x+8\] so
\[f(-15)=-15+8=-7\]

Answer 13

and that is your "final answer" although i sense there might be some confusion as to how we got it

Answer 14

haha yes just a tad

Answer 15

ok we can try another one if you like
would you like to post one, or would you like me to make one up?

Answer 16

Let f(x) = 9x – 2 and g(x) = –x + 3. Find f(g(x)).

Answer 17

another method would be to just insert g(x) into the x-spot of f(x); then make x=2 and solve

or in this last case, leave it as is

Answer 18

ok so once again we work from the inside out. we want "f of g of x"

Answer 19

f(g(x)) = 9(g(x))-2

replace g(x) with what it equals

Answer 20

now in this example we do not want
\[f(g(2))\] which is a number, but rather we want
\[f(g(x))\] which is a function.
step one is to replace the general
\[g(x)\] which could be any function by the specific one you have, namely
\[g(x)=-x+3\] so we write
\[f(g(x))=f(-x+3)\]

Answer 21

so far not much. now comes the only confusing part. and it is confusing because of all the x's you see
\[f(x)=9x-2\] but the "x" is not important. it means "multiply by 9, subtract 2"

Answer 22

it the use of "x" for the independant variable in both cases that makes the notation a bit confusing to begin with

Answer 23

so we could just as well write
\[f(\alpha)=9\alpha -2\] or
\[f(\heartsuit)=9\heartsuit -2\]

Answer 24

and our job now is to replace
\[x\] or
\[\alpha\]or
\[\heartsuit\] by
\[-x+3\] (and don't forget parentheses) so you get
\[f(-x+3)=9(-x+3)-2\]

Answer 25

so your answer would be -9x-2??

Answer 26

then a tiny bit of algebra to clean this up. i will write it in one line, like you would if you were handing it in
\[f(g(x))=f(-3x+3)=9(-x+3)-2=-9x+27-2=-9x+25\]

Answer 27

oooh okayyy

Answer 28

you have to multiply EVERYTHING in the parentheses by 9

Answer 29

to recap
1) replace g(x) by the specific on
2) replace the "x" in f(x) by g(x) using parentheses
3) use the distributive property
4) combine like terms

the last two steps are algebra steps

Answer 30

thank you<3