Question

ok i have NO idea how to do this

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

Answer 1

@TheSmartOne

Answer 2

Plug in 2 into g(x) and tell me what you get. And then plug that new number into f(x)

That's essentially what f(g(2)) means

Answer 3

ummmmmmmmmmmmmmmmmmmmmmmmm ok ill try but still confused

Answer 4

\[g(2)=(2)2-6(2)-7\]

Answer 5

^so kinda like this

Answer 6

Let use different variables

P(a)
And let's say a actually was the same thing as Q(b)

So when we say P(Q(b))
That's the same thing as P(a) because a = Q(b)

Answer 7

.......

Answer 8

Yes

Answer 9

f(2) is a number
g(2) is also a number
f(a number) is another number
f(g(2)) is f(a number) is a number
you were off to a good start

What do you get for g(2)?

Answer 10

I was trying to explain why we substitute and substitute again, but uh hopefully nuts has a better response

Answer 11

i don't x'd

Answer 12

ok im still confused give me a sec

Answer 13

just tell us, what you get for g(2)

Answer 14

do i answer g(2) the same as i did in the last question

Answer 15

does g(x) turn into y like f(x) does

Answer 16

just follow what we say, it will make more sense after
\(\color{#0cbb34}{\text{Originally Posted by}}\) @AnimeGhoul8863
\[g(2)=(2)^2-6(2)-7\]
\(\color{#0cbb34}{\text{End of Quote}}\)
what do you get as a final answer for g(2)?

Answer 17

so yes on g(x) turns into y or no

Answer 18

i think she's yours now tso since i can't deal with people that can't follow instructions

Answer 19

WHAT I AM FOLLOWING UR INSTRUCTIONS ITS JUST U DONT GIVE GOOD DETAILS

Answer 20

you should be getting a single number for g(2), no? what is that number

Answer 21

I asked is g(x) the same as F(x) since f(x) turns into y

Answer 22

Lolol

Just plug in 2 into g(x) and solve

Answer 23

im so confused how the heck do i solve g(2)

Answer 24

thats what im asking

Answer 25

Let f(x) = x + 8 and g(x) = x^2 − 6x − 7. Find f(g(2)).

g(2)=2^2-6*2-7

Answer 26

g(x) and f(x) are two different functions

So like you're used to thinking f(x) is another way of saying y, so is g(x) but it's a different y so you can use any letter to replace it. If that makes any sense

Answer 27

it's a notational thing, f, g, h tend to be letters used for functions

Answer 28

i keep thinking but i still cant understand how to calculate this

Answer 29

the whole thing, or just g(2)?

Answer 30

everything i try i get nonsense or decimals

just g(2) so far

Answer 31

show us some steps

Answer 32

we can easily show you how to do it but it might help you a bit more for us to clear up misconceptions

Answer 33

g(x) =x2 -6x -7
f(g(x))= f(x2 - 6x) -7
??? ^this is pretty much guessiing cause i dont know this

Answer 34

noooo just focus on calculating g(2) first

Answer 35

i thought thats what i was doing

Answer 36

x is a placeholder letter... in f(x) and g(x) the x's are referring to separate occasions... it's like how an x in one problem isn't the same as an x in another problem.

right now all you need to do is to start by calculating g(2)... forget that f(x) exists for a moment

Answer 37

but HOW do i calculate G(2)

Answer 38

g(x)=x^2-6x-7

Answer 39

ok

Answer 40

i still dont understand

Answer 41

i know what the problem looks like i need help solving it

Answer 42

what doesn't make sense

Answer 43

the whole g(2)

Answer 44

what about g(2) doesn't make sense? what it's supposed to mean?

Answer 45

how i calculate it and solve it

Answer 46

if I told you,
f(x)=x^2-6x-7, and asked you what f(2) was, could you calculate it?

Answer 47

everything in this equation i dont understand

Answer 48

give me a second and try

Answer 49

ok i tried but got no where

Answer 50

its not the same i cant do it

Answer 51

can you write down a few of your steps?

Answer 52

f(x)=x^2-6x-7
y=x2-6x-7
x=y2-6y-7
+6 +6

Answer 53

you don't need to switch any variables...

Answer 54

all you have to do is plug in 2 for x, like you were starting to from before:
\(f(2)=(2)^2-6(2)-7=4-12-7=...\)

Answer 55

4-12-7=-15

Answer 56

and that's the same number as g(x), because you evaluated "x^2-6x-7", right?

Answer 57

yes? i evaluated it making it -15 right

Answer 58

yup.
so knowing that g(2) is -15, what is f( g(2) )?

Answer 59

i'm using the f(x) from the problem, the f(x)=x+8. Hopefully I don't confuse you too much with the stuff earlier.

Answer 60

ummmmmmmmmmmmmmmmmmmm