Question

perform the indicated function evaluations for:
f(x)=10x-3

f(12-x)....?

Answer 1

Replace 'x' with '12-x' to get


f(x)=10x-3


f(12-x)=10(12-x)-3


Now simplify and tell me what you get.

Answer 2

120x-3 .........?

Answer 3

10(12-x) - 3

10*12-10*x - 3

120 - 10x - 3

117x - 10x

-10x + 117


So f(12-x)= -10x+117

Answer 4

So somehow you mixed up the terms

Answer 5

soo I probably messed up on f(t^2+2) ....

Answer 6

perhaps, but idk since I can't see what you got

Answer 7

I got 10t^2+20-3 for that one

Answer 8

f(x)=10x-3

f(t^2+t)=10(t^2+t)-3

f(t^2+t)=10t^2+10t-3

Answer 9

and you can't go further because there are no like terms to combine

Answer 10

my problem with these types of equations is that I always end up multiplying whats outside of the parenthesis with whats inside

Answer 11

thats how I got 20 instead of 10

Answer 12

well you're sorta on the right track because you do multiply that 10 sitting out front the parenthesis with everything inside

Answer 13

so why wouldn't I multiply it with the 2 thats sitting inside the parenthesis?

Answer 14

because you only multiply the coefficients, not the exponents

Answer 15

since 10 times t^2 = 10t^2 and NOT 20t^2, 20t or 20

Answer 16

so just ignore the 2 right

Answer 17

pretty much

Answer 18

ok thankyou so much!

Answer 19

np

Answer 20

ok so would f(x-h) be 10x+10h-3...?

Answer 21

f(x)=10x-3

f(x-h)=10(x-h)-3

Got this so far?

Answer 22

yes

Answer 23

ohh wait I made a mistake its supposed to be a plus sign not a minus

Answer 24

Now distribute

f(x)=10x-3

f(x-h)=10(x-h)-3

f(x-h)=10x-10h-3

Answer 25

yeah thats what I got except its a plus sign between 10x and 10h

Answer 26

i see, so you lost a negative sign somewhere

Answer 27

do you mind helping me with another one real fast..?

Answer 28

sure thing

Answer 29

ok its sorta the same kind of problem,
h(y)=4y^2-7y+1
h(6z)...?

Answer 30

Start with

h(y)=4y^2-7y+1

and replace EVERY 'y' with '6z' to get

h(6z)=4(6z)^2-7(6z)+1

Then simplify

Answer 31

12z^2-42z+1

Answer 32

(6z)^2 = 36z^2

then 4*36z^2 = 144z^2

So it should be 144z^2-42z+1

Answer 33

I thought after I did that I would then square 12 which would be 144

Answer 34

how are you getting 12?

Answer 35

or 12^2 ?

Answer 36

sure 12^2 = 144 and 4*36 = 144, but I'm not seeing how you got 12

Answer 37

yeap you're right I was multiplying wrong

Answer 38

i gotcha, i'm glad you caught your mistake

Answer 39

haha yeah. ok I'm gonna work one out on my own and you tell me if I get it right?

Answer 40

alright sounds great

Answer 41

cool! ok this one looks hard ...but I'll give it a try...

its for the same problem ....
h(1-3y)

4(1-3y)^2-7(1-3y)+1= 4-12y^2-7-21+1

Answer 42

and Idk if I should keep simplifying...?

Answer 43

it might help to just focus on (1-3y)^2

(1-3y)^2

(1-3y)(1-3y)

1(1-3y)-3y(1-3y)



So simplify 1(1-3y)-3y(1-3y) and tell me what you get

Answer 44

3y-3y-9y^2

Answer 45

Ik thats not right...BUtik you have to multiply it with whats int the parenthesis..

Answer 46

1(1-3y)-3y(1-3y)

1-3y-3y-9y^2

1 - 6y - 9y^2

Somehow you lost a 1

Answer 47

YEAH I did. I make the littlest mistakes -__- Ok where did the 6 some from?

Answer 48

-3y - 3y = -6y

Answer 49

since -3-3 = -6

Answer 50

ok I get it now

Answer 51

alright great

Answer 52

so

4(1-3y)^2-7(1-3y)+1

becomes

4(1 - 6y - 9y^2)-7(1-3y)+1

Answer 53

thankyou!

Answer 54

you're welcome, tell me what you get when you simplify that

Answer 55

ok

Answer 56

sorry for the wait. ok so I got 4-24y-81y^2-7-21-1...?

Answer 57

you mean -36y^2 ?

and

-21y?

Answer 58

oh and that -1 at the end should be +1

Answer 59

oh and sry, -7 times -3y is +21y

Answer 60

let me write it all out

4(1 - 6y - 9y^2)-7(1-3y)+1

4 - 24y - 36y^2 - 7 + 21y + 1

Answer 61

now combine like terms

Answer 62

4-36y^2-7+45y+1

Answer 63

??

Answer 64

-24+21 = -3

Answer 65

so -24y + 21y = -3y

Answer 66

4-7+1 = -3+1 = -2

Answer 67

4 - 24y - 36y^2 - 7 + 21y + 1

-36y^2 - 3y - 2

Answer 68

Does it matter which one I subtracted or added first?

Answer 69

with subtraction order matters, so yes

Answer 70

-24+21

is the same as

21 - 24

Answer 71

ok...I just got lost.....

Answer 72

where

Answer 73

point which step

Answer 74

point out*

Answer 75

at this point...4-7+1 = -3+1 = -2

Answer 76

4 - 7 is -3

Answer 77

so

4-7+1

is the same as

-3+1

Answer 78

then -3+1 becomes -2

Answer 79

So in the end, 4-7+1 = -2

Answer 80

one sec

Answer 81

Here's the full and complete problem

4(1-3y)^2-7(1-3y)+1

4[ (1-3y)(1-3y) ]-7(1-3y)+1

4(1 - 6y + 9y^2)-7(1-3y)+1

4 - 24y + 36y^2 - 7 + 21y + 1

36y^2 - 3y - 2

Answer 82

So

4(1-3y)^2-7(1-3y)+1

simplifies to

36y^2 - 3y - 2

Answer 83

how did you get 36y^2-3y-2 as your final answer..... I see how you got 36....but where did 3 and 2 come from...

Answer 84

Hopefully this is a bit clearer

4(1-3y)^2-7(1-3y)+1

4[ (1-3y)(1-3y) ]-7(1-3y)+1

4(1 - 6y + 9y^2)-7(1-3y)+1

4 - 24y + 36y^2 - 7 + 21y + 1

36y^2 (- 24y+21y) + (4- 7+ 1 )

36y^2 - 3y - 2

Answer 85

If not, let me know

Answer 86

got it! makes sense

Answer 87

alright great

Answer 88

thankyou so much ! you're a great teacher.

Answer 89

why thank you, I'm glad I could help you out

Answer 90

is it ok if you help me with a couple more problems. Im trying to get the hang of this.

Answer 91

sure go for it

Answer 92

this one is h(y+k)

I got
4(y+k)^2-7(y-K)+1
=4(y+k)^2-7(y+7yk+k)+1
=4y^2+4k^2-7y+49yk+7k+1

Answer 93

h(y+k) ?? not f(y+k) ??

Answer 94

wait, we're talking about the same function

4x^2 - 7x + 1

right??

Answer 95

nooo its h

Answer 96

oh ok, but it's still 4x^2 - 7x + 1 right?

Answer 97

yesss

Answer 98

ok thanks