Question

6. The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2.
This is my h function
h(x)=10x-5
my f(x)
f(x)=9x+6

Answer 1

@ganeshie8

Answer 2

i need help

Answer 3

1. Two Martians, Splott and Fizzle, have solved the equation 2x + 4 = –3x + 14. Examine the work of Splott and Fizzle. Identify any errors in the Martians’  calculations and explain, using complete sentences, what corrections they should make.
One mistake that Splott made was that he should have subtracted 4 not added it to +4, done the same thing to 14, subtract 4 not add it then he should change 18 to 10 and change the ange to x=2 since 10/5 is 2
For Fizzle he just did te math wrong for 4-14 he put -12, he should have put -10. which would then make the problem -10=-5x. Then he should divide -5by both sides to get the answer 2.
Splott
Fizzle
2x + 4 = –3x + 14
2x + 4 = –3x + 14
2x + 4 + 3x = –3x + 14 + 3x
2x + 4 – 2x = –3x + 14 – 2x
5x + 4 = 14
4 = 14 – 5x
5x + 4 + 4 = 14 + 4
4 – 14 = 14 – 5x – 14
5x = 18
–12 = –5x
5x/5=18/5
–12 + 5 = –5x + 5

X= 18/5
–7 = x
2. Create your own function to teach the Martians about functions. Your function must contain at least two different operations. f(x)=6x+9

3. Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function. The reason this is and legit function is that for every x value there is a unique y value.
4. Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sentences.
F(3)=6(3)+9
f(3)=18+9
f(3)=27
5. Using complete sentences, describe to the Martians how to find the inverse of your function.
First you would take the y value 27 and replace f(3) with it. And then make the equation 27=6x+9. Then you subtract 9 from both sides, like so 27-9=6x+9-9. You are then left with this, 27-9=6x. Then you divide 6 by both sides, to get this, 27-9/6=6x/6. Then after tyou do the division and you are left with 27-9/6=x.

6. The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2.
h(x)=10x+5

Answer 4

i really only need help with the last question

Answer 5

i dont understand how to start it

Answer 6

You have :
```
h(x)=10x-5
f(x)=9x+6
```

Answer 7

yes

Answer 8

you wanto to find whether ` f(h(x))` and `h(f(x)) ` result in the same number or not for some value of `x`. Is that right ?

Answer 9

yes and i dont understand how to

Answer 10

or how to explain it

Answer 11

Lets find `f(h(x))` first,
we need to pick some value for `x`, lets say x=1 ?

Answer 12

```
h(x)=10x-5
f(x)=9x+6
```

to find `h( f(1) ) ` , you need to work `f(1)` first

Answer 13

f(1) = ?

Answer 14

f(1)=9(1)+6

Answer 15

yes, simplify

Answer 16

f(1)=9+6
-6
f(1)=9

Answer 17

NO.

f(1)=9(1)+6
= 9 + 6
= 15


so the value of f(1) is 15

Answer 18

oh ok so f(1)=15

Answer 19

So, h( f(1) ) = h(15)
= ?

Answer 20

whats the value of h(15) ?

Answer 21

see this is what confuses me

Answer 22

you have
```
h(x)=10x-5
```


plugin x = 15 to get h(15) :

```
h(15) = 10*15 - 5
= ?
```

Answer 23

h(15)=10*15-5
=150-5
=145
h(15)=145

Answer 24

Yes! so overall we have :

h( f(1) ) = h( 15 )
= 145


fine ?

Answer 25

similarly, can you find the value of `f( h(1) )` ?

Answer 26

f(h(1))=f(145)
or am i wrong

Answer 27

or f(h(1))=f(15)
Which one is right?

Answer 28

to find `f( (h(1) )`, you need to work `h(1)` first

h(1) = ?

Answer 29

h(1)=10(1)-5
=10-5
h(1)=5

Answer 30

yes!

f( h(1) ) = f( 5 )
= ?

Answer 31

whats the value of f(5) ?

Answer 32

f(5)=10(5)-5
=50-5
f(5)=45

Answer 33

Correct!
so

f( h(1) ) = f( 5 )
= 45

Answer 34

we have got :

`h(f(1)) = 145`
and
`f(h(1)) = 45`


Clearly they're NOT same right ?

Answer 35

True.
but now i have to fiigure out how to put that all into complete sentences

Answer 36

show the work above and conclude that `h(f(x))` and `f(h(x))` need not be same

Answer 37

oh ok thanks man

Answer 38

yw :)