Question

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

Answer 1

(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?

Answer 2

A. -53
C.23
D.3

Answer 3

No i have no clue

Answer 4

@satellite73

Answer 5

Could you help @jim_thompson5910

Answer 6

@SolomonZelman

Answer 7

g(x) = -4x + 3

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

g(-5) = ??

Answer 8

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

Answer 9

Oh i know and i defiantly want the help

Answer 10

(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

Answer 11

20+3

Answer 12

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

Answer 13

Oh sorry i was replying to what @jim_thompson5910 started

Answer 14

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

agreed?

Answer 15

correct

Answer 16

f(g(-5)) becomes f(23)

after you replace g(-5) with 23

Answer 17

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

Answer 18

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

Answer 19

so the end result should be

-2(insert g(x) function here)-7

Answer 20

then combine like terms and evaluate when x = -5

Answer 21

im lost

Answer 22

Is the answer 23?

Answer 23

no

Answer 24

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

Answer 25

ok im ready to learn the rest

Answer 26

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

Answer 27

No i got lost after we got f(23)

Answer 28

To calculate f(23), replace every x in f(x) with 23


f(x) = -2x - 7

f(23) = -2*23 - 7

f(23) = ??

Answer 29

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

Answer 30

it's just like the g(x) one

Answer 31

-46

Answer 32

f(23)=-46-7

Answer 33

keep going

Answer 34

almost there

Answer 35

46-7=39

Answer 36

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

Answer 37

opps wrong

Answer 38

-53

Answer 39

yes!

Answer 40

good

Answer 41

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

Answer 42

yay we did it

Answer 43

yes that would be great

Answer 44

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

Answer 45

Can you guys help me solve another @UsukiDoll @jim_thompson5910

Answer 46

sure

Answer 47

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

Answer 48

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

Answer 49

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

Answer 50

so is x -2?

Answer 51

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

Answer 52

so X^2+X+2?

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

Ok so where do we go from this?

Answer 57

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)

Answer 58

2x2=4

Answer 59

2x+2x=4X

Answer 60

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

Answer 61

2

Answer 62

\[x ^{2}\]

Answer 63

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

Answer 64

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

Answer 65

25-20+4=9

Answer 66

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

Answer 67

Thank you very much