Question

Let f(x)=-2x+4 and g(x)=-6x-7. Find f(x) - g(x).

Please help me out! Is this not a problem of factoring? (-2x-4)-(-6x-7) I think? I just don't know how to get to the answer. Please walk me through this step by step!

Answer 1

I need help with this one too, if possible?
f(x)=3x-7 and g(x)=-2x-6. Find (f o g)(4). I literally have no clue what to do.

Answer 2

You only have to find the difference between this functions. In this case,
\[f(x)=-2x+4; \ \ g(x)=-6x-7\Rightarrow f(x)-g(x)=(-2x+4)-(-6x-7)=\\
-2x+4+6x+7=4x+11\]

Answer 3

@John_ES that's what I was told the answer was, so now I can see exactly how it got to be there. Thank you so much! Do you know how to do this one?
f(x)=3x-7 and g(x)=-2x-6. Find (f o g)(4).
I haven't been taught this, I actually have no idea why it's even on this practice sheet.

Answer 4

Let's see an easier example. Suppose you have
\[f(x)=x^2\] and
\[g(x)=2x+1\]And you need
\[(f\circ g)(x)\]
Then, then only thing you need to do is put the function g(x) in the x of the function f(x). Let's do it,
\[(f\circ g)(x)=f(g(x))=(g(x))^2=(x+1)^2\] And that's all.

Answer 5

Let's see the problem. In your case, you have,
\[f(x)=3x-7 ;\ \ g(x)=-2x-6\] So,
\[(f\circ g)(x)=f(g(x))=3g(x)-7=3(-2x-6)-7=-6x-25\]And,
\[(f\circ g)(4)=-6\cdot4-25=-49\]

Answer 6

Where exactly does the 3g come from?

Answer 7

Your function f(x) is 3x-7.

So if you substitute x for g(x) then you have 3g-7. Do you see it?

Answer 8

Ahhhhh, yes. I see it now. I'm totally clear on it. Thank you so much, you're a lifesaver.

Answer 9

;)