Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (f o g)(-5)

- anonymous

Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (f o g)(-5)

- katieb

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- jim_thompson5910

(f o g)(-5) is the same as f(g(-5))
the first task is to find g(-5). Do you know how to do this?

- anonymous

A. -53
C.23
D.3

- anonymous

No i have no clue

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## More answers

- anonymous

- anonymous

Could you help @jim_thompson5910

- anonymous

- jim_thompson5910

g(x) = -4x + 3
g(-5) = -4(-5) + 3 ... replace every x with -5
g(-5) = ??

- misssunshinexxoxo

On OS we help people learn; Jim is trying to make sure you are understanding this

- anonymous

Oh i know and i defiantly want the help

- UsukiDoll

(f o g)(-5)
well first let's do (f o g ) which means that the g(x) equation is placed inside the f(x) equation

- anonymous

20+3

- UsukiDoll

whoa... let's do this step by step

- anonymous

Oh sorry i was replying to what @jim_thompson5910 started

- jim_thompson5910

so you should find that g(-5) = 23
agreed?

- anonymous

correct

- jim_thompson5910

f(g(-5)) becomes f(23)
after you replace g(-5) with 23

- jim_thompson5910

now follow the same basic steps to calculate f(23)

- UsukiDoll

ok it's ok didn't see that :)
anyway given the functions f(x) = -2x-7 and g(x) = -4x+3
we need to place g(x) =-4x+3 into the f(x)
so for every x in f(x) the g(x) takes it's place

- UsukiDoll

so the end result should be
-2(insert g(x) function here)-7

- UsukiDoll

then combine like terms and evaluate when x = -5

- anonymous

im lost

- anonymous

Is the answer 23?

- jim_thompson5910

no

- UsukiDoll

I agree with jim there's more to be done...

- anonymous

ok im ready to learn the rest

- UsukiDoll

k.. so did you already place your g(x) into your entire f(x) function?

- anonymous

No i got lost after we got f(23)

- jim_thompson5910

To calculate f(23), replace every x in f(x) with 23
f(x) = -2x - 7
f(23) = -2*23 - 7
f(23) = ??

- UsukiDoll

that means x = 23 evaluate the f(x) function

- jim_thompson5910

it's just like the g(x) one

- anonymous

-46

- anonymous

f(23)=-46-7

- jim_thompson5910

keep going

- UsukiDoll

almost there

- anonymous

46-7=39

- UsukiDoll

we have two negative numbers so the negative numbers are supposed to increase, not decrease

- anonymous

opps wrong

- anonymous

-53

- UsukiDoll

yes!

- jim_thompson5910

good

- UsukiDoll

do you want to see another method of solving this equation as a reference?

- anonymous

yay we did it

- anonymous

yes that would be great

- UsukiDoll

ok so here's how I would tackle this problem
(f o g ) (-5)
first I will tackle f o g portion and then evaluate when x = -5
so f o g means that we place our g(x) function inside all x's of the f(x) function
f(x) = -2x-7 and g(x) = -4x+3
f o g
-2(-4x+3)-7
distribute the -2
8x-6-7
8x-13
so our f o g = 8x-13
now evaluating when x = -5
f o g (-5) = 8(-5)-13
= -40-13
= -53

- anonymous

Can you guys help me solve another @UsukiDoll @jim_thompson5910

- UsukiDoll

sure

- anonymous

Let f(x) = x + 2 and g(x) = x2 Find ( g o f)(-5)

- UsukiDoll

\[\large f(x) = x+2, g(x) = x^2 \]

- UsukiDoll

this is similar to the previous problem. while our x still remains the same
g o f means that we place our entire f(x) function inside the x's of the g(x) function
so
g o f = (insert f(x) here)^2

- anonymous

so is x -2?

- UsukiDoll

our f(x) = x+2 and we need place it inside g(x). Since g(x) =x^2
g o f = (f(x) function)^2

- anonymous

so X^2+X+2?

- UsukiDoll

\[g o f =(x+2)^2 \]
that second power means write (x+2) two times
after that, we need to use FOIL to expand

- anonymous

your gonna have to hold my hand on this one cuz im totally lost lol im sorry

- UsukiDoll

alirght..
so we write (x+2) two times
(x+2)^2 means (x+2)(x+2)
now using FOIL
(x)(x)+2(x)+2(x)+(2)(2)
so what's 2 x 2
2x + 2x
and x times x I guess that's the closest way of notating multiplication

- anonymous

Ok so where do we go from this?

- UsukiDoll

first tell me what 2 x 2 is
then tell me what 2x+2x is .. I will factor out the x to make it easier x(2+2)

- anonymous

2x2=4

- anonymous

2x+2x=4X

- UsukiDoll

mhm
last one what is (x)(x) . I'll make this easier by rewriting it and using the addition exponential rule,
\[\large (x)(x) \rightarrow x^1x^1 \rightarrow x^{1+1}\]
so you just have to solve for the exponent part. what is 1+ 1

- anonymous

2

- anonymous

\[x ^{2}\]

- UsukiDoll

yes so now we have \[g o f =x^2+4x+4 \]

- UsukiDoll

so now we evaluate this when x = -5.
so replace all x's with -5

- anonymous

25-20+4=9

- UsukiDoll

\[g o f (-5) =(-5)^2+4(-5)+4\]
\[g o f (-5) =25-20+4 \rightarrow 5+4 = 9 \]
correct

- anonymous

Thank you very much

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