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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)

- leozap1

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- schrodinger

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- jango_IN_DTOWN

HI... I can help you

- leozap1

Okay... How do I solve this?

- 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

\[ax-bx=(a-b)x\]

- jango_IN_DTOWN

Just using this formula we did the sum here

- jango_IN_DTOWN

@leozap1 did you get it?

- leozap1

I'm trying just a sec

- 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

yeah correct

- jango_IN_DTOWN

-(-6)=6

- leozap1

So it would be -2x-6x-4-7?

- jango_IN_DTOWN

no

- jango_IN_DTOWN

wait

- leozap1

Ohh so since they are already negative, it makes them positive?

- 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

|dw:1444742322049:dw|

- 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

nothing more... If you want an explanation more in depth, in algebraic sense, then I can offer

- leozap1

I think I get it, I'll try working out other problems now. Thank you for all the help.

- 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

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

Is it suppose to be multiplication? If so I can figure it out, if not I have no idea...

- jango_IN_DTOWN

HI... Are you still there?? My internet connection went down

- leozap1

Yea.

- 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

@leozap1

- leozap1

No, sorryy

- jango_IN_DTOWN

Ok.. Here we go

- jango_IN_DTOWN

fog(x)=f(g(x))

- leozap1

Okay so it would be f(g(x)) = 3x-7-2x-6?

- jango_IN_DTOWN

f(g(x))=f(-2x-6)=3(-2x-6)-7=-6x-18-7=-6x-25

- 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

So the answer would be -49?

- jango_IN_DTOWN

answer is -6x-25

- leozap1

f(g(x)) = -6x-25
f(g(x)) , if x=4 or (ƒ ∘ g)(4) ------> -6(4) -25 = -45???

- jango_IN_DTOWN

-49

- jango_IN_DTOWN

-6(4)-25=-24-25=-49

- leozap1

That's what I meant, sorry.

- leozap1

Would we have to do that, or just leave it like it was?

- 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

So like this?

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