Question

The Martians ask you to explain one last thing, Ultimate Math Ambassador. Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will always result in the same number. You will use the inverse function that you created in problem number 5 for g(x).

Answer 1

Our inverse function will be x-6/10 = g(x) and our normal function f(x) = 10x + 6

Answer 2

any1 explain it to me lol?

Answer 3

Don't use \(f(x) = \sqrt{x}\;and\;g(x) = x^{2}\). The Martians will expose your error.

Answer 4

what?

Answer 5

I can't see the definitions created in Problem 5, so I just made some up to emphasize an important point.

Answer 6

i need help pleasing the martians lol

Answer 7

I know i'm suppose to insert g(x) into F(x) and vise versa but i need help placing them and solving

Answer 8

First off, your notation needs improvement.

"x-6/10 = g(x)"

You do not mean this. You mean (x-6)/10 = g(x) -- THEN the Martians will be happy. Martians know about the Order of Operations.

The rest of the problem goes to your understanding of the notation.

Given g(x) = (x-6)/10,

What is g(3)?
How about g(3/2)?
What about g(ZR)?
Maybe g(dog)?

Answer 9

sorry about the notations, g(3) is..

g(3) = (3-6)/10
g(3) = 3/10
*10
g3 = 30?

Answer 10

It's not a matter of sorry. It's a matter of learning.

g(3) = -3/10

Try g(3/2)

You must understand this notation and do the algebra perfectly. No room for errors.

Answer 11

alright
g(3/2) = (x-6)/10

Answer 12

i'm a bit confused with inputing 3/2

Answer 13

This is why we are doing this drill. Do not be confused. Just substitute whatever it is.

g(3/2) = ((3/2)-6)/10 = ((3/2)-(12/2))/10 = ((3-12)/2)/10 = (-9/2)/10 = -9/20

Answer 14

how did u get (3/2) - (12/2)/10?

Answer 15

First, understand the notation and just substitute away.
Second, sift through all the algebra and arithmetic.

I didn't get that. I said, ((3/2)-(12/2))/10. You forgot your Order of Operations, again.

It's just addition. Common denominator and all that? 6 = 12/2

Answer 16

so you changed 6 to 12/2 so that u could simplify it with 3/2?

Answer 17

Right. Addition and Subtraction of fractions works that way. You should be VERY good at adding fractions before you get to algebra. You may wish to review more formally and get it up to speed.

Answer 18

alright and we need to add 12/2 to 3/2 right?

Answer 19

and to add it we change 3/2 to 12/4 and then add 12/2 to 12/4 then add them to make 12/6 which simplifies to 2?

Answer 20

What? This is not encouraging. Let's remember how to add fractions.

\(\dfrac{3}{2} - 6 = \dfrac{3}{2} - \dfrac{12}{2} = \dfrac{3-12}{2} = \dfrac{-9}{2}\)

Notice how the denominator doesn't do anything. If you add 1 dog and 2 dogs, you get =3 dogs. This is like the denominator. 1 half plus 12 halves is 13 halves. It desn;t magically change to 4ths.

Answer 21

* doesn't

So, g(f(x)) = (f(x) - 6)/10

Substitute the definition for f(x)

g(f(x)) = (f(x) - 6)/10 = ((10x+6) - 6)/10

Simplify and it is hoped that you are done. You may be called upon to do the same for f(g(x)).

Good luck. I need to go.

Answer 22

Our inverse function will be x-6/10 = g(x) and our normal function f(x) = 10x + 6 if i remember right..

Answer 23

No. Absolutely not. g(x) = (x-6)/10. Structure should be meaningful!