leozap1
  • leozap1
*Fan & Medal* Please explain how I can do this, I want to learn it. Let f(x) = -2x + 4 and g(x) = -6x - 7. Find f(x) - g(x)
Mathematics
schrodinger
  • schrodinger
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jango_IN_DTOWN
  • jango_IN_DTOWN
HI... I can help you
leozap1
  • leozap1
Okay... How do I solve this?
jango_IN_DTOWN
  • jango_IN_DTOWN
Hmm... you should find f(x)-g(x)=(-2x+4)-(-6x-7)=-2x+6x+4+7=4x-11

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jango_IN_DTOWN
  • jango_IN_DTOWN
\[ax-bx=(a-b)x\]
jango_IN_DTOWN
  • jango_IN_DTOWN
Just using this formula we did the sum here
jango_IN_DTOWN
  • jango_IN_DTOWN
@leozap1 did you get it?
leozap1
  • leozap1
I'm trying just a sec
leozap1
  • leozap1
On this part "2x+6x+4+7" aren't we suppose to subtract? It says to find f(x) - g(x)
jango_IN_DTOWN
  • jango_IN_DTOWN
yeah correct
jango_IN_DTOWN
  • jango_IN_DTOWN
-(-6)=6
leozap1
  • leozap1
So it would be -2x-6x-4-7?
jango_IN_DTOWN
  • jango_IN_DTOWN
no
jango_IN_DTOWN
  • jango_IN_DTOWN
wait
leozap1
  • leozap1
Ohh so since they are already negative, it makes them positive?
jango_IN_DTOWN
  • jango_IN_DTOWN
the expression of f(x) will not be changed. but the expression of g(x) will be its negative.. g(x)=-6x-7 so -g(x)=-(-6x-7)=6x+7
jango_IN_DTOWN
  • jango_IN_DTOWN
|dw:1444742322049:dw|
jango_IN_DTOWN
  • jango_IN_DTOWN
leozap1
  • leozap1
Oh, that makes more since. So is the answer 4x+11, or is there anything else needing to be done?
jango_IN_DTOWN
  • jango_IN_DTOWN
nothing more... If you want an explanation more in depth, in algebraic sense, then I can offer
leozap1
  • leozap1
I think I get it, I'll try working out other problems now. Thank you for all the help.
jango_IN_DTOWN
  • jango_IN_DTOWN
ok.. remember f(x)-g(x)=f(x)+{-g(x)} where -g(x) is when the expression of g(x) is multiplied by -1
leozap1
  • leozap1
This is one of the other problems, and I honestly have no idea about it ether. If you know how to do it I can create a new post so you will get another medal.
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leozap1
  • leozap1
Is it suppose to be multiplication? If so I can figure it out, if not I have no idea...
jango_IN_DTOWN
  • jango_IN_DTOWN
HI... Are you still there?? My internet connection went down
leozap1
  • leozap1
Yea.
jango_IN_DTOWN
  • jango_IN_DTOWN
No that's not multiplication. For this thing you need to know composition of mappings;. Are you familiar with this term?
jango_IN_DTOWN
  • jango_IN_DTOWN
leozap1
  • leozap1
No, sorryy
jango_IN_DTOWN
  • jango_IN_DTOWN
Ok.. Here we go
jango_IN_DTOWN
  • jango_IN_DTOWN
fog(x)=f(g(x))
leozap1
  • leozap1
Okay so it would be f(g(x)) = 3x-7-2x-6?
jango_IN_DTOWN
  • jango_IN_DTOWN
f(g(x))=f(-2x-6)=3(-2x-6)-7=-6x-18-7=-6x-25
jango_IN_DTOWN
  • jango_IN_DTOWN
See we are given the value of f(x).. now when you need to calculate f(g(x)) just replace x by g(x) in the expression of f(x)
leozap1
  • leozap1
So the answer would be -49?
jango_IN_DTOWN
  • jango_IN_DTOWN
answer is -6x-25
leozap1
  • leozap1
f(g(x)) = -6x-25 f(g(x)) , if x=4 or (ƒ ∘ g)(4) ------> -6(4) -25 = -45???
jango_IN_DTOWN
  • jango_IN_DTOWN
-49
jango_IN_DTOWN
  • jango_IN_DTOWN
-6(4)-25=-24-25=-49
leozap1
  • leozap1
That's what I meant, sorry.
leozap1
  • leozap1
Would we have to do that, or just leave it like it was?
jango_IN_DTOWN
  • jango_IN_DTOWN
First you need to calcuate f(g(x)) in terms of x and the plug the numeric value of x, as it is given in this problem
leozap1
  • leozap1
So like this?

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