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apologiabiology
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If \(f(x)= \frac{1}{x-2}\) and (fg)'(1)=6 and g'(1)=-1, then g(1)=

A5
B-7
C7
D5
E8

(note: (fg)'(1) means the derivitive of f(x)g(x) at x=1)

wow, the answer is 5, but why?

ples show all work and logic (don't just refernce to an online solver)

Verified Answer :

I think, the answer will be -7

We have:
f(x)=1/(x-2)
g(x)
Then:
(fg)(x)=[1/(x-2)](g(x))=g(x)/(x-2)
Now; we calculate: (fg)(x)
Remember: (u/v)=(uv-vu´)/v²
Therefore:

(fg)´(x)=[g´(x)(x-2) - 1g(x)]/ (x-2)²
We know that:
g´(1)=-1
(fg)´(1)=6
Therefore:
6=[-1*(1-2)-g(1)]/(1-2)²
6=[1-g(1)]/1
6=1-g(1)
-g(1)=6-1
g(1)=-5

Answer: B. -5

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