let f be defined by f(x) = x-4 and g be defined by g(x) = {x^2 - 16 /x+4 ,x ≠ -4 and k , x = -4 } . find k such that f(x) = g(x) for all x.

Question

let f be defined by f(x) = x-4 and g be defined by g(x) = {x^2 - 16 /x+4 ,x ≠  -4 and k ,  x = -4 } . find k such that f(x) = g(x) for all x.

anonymous · Answer

x=0 is the only answer I think!

anonymous · Answer

how ? .. can you solve ?

anonymous · Answer

yes

anonymous · Answer

k=0....for x ≠  -4 we already have g(x) = {x^2 - 16 /x+4 =(x-4)*(x+4)/x+4
for x ≠  -4 g(x)=x-4 
for x=-4  therefore  g(-4)=k=f(-4)=0

anonymous · Answer

k$$x-4=x ^{2}-16/(x+4)   =>     x-4 = (x ^{3}+4x-16)/x+4   $$
$$x ^{2}-16 = x ^{3}+4x-16   =>  -x ^{3}-4x+x ^{2}=0$$
$$-x(x ^{2}+4-x)=0 =>x=0$$

anonymous · Answer

@mas_gh90 Sorry but, you made a mistake !

anonymous · Answer

thanks!can u explain more?

anonymous · Answer

first , the question is to find k not x.

anonymous · Answer

@mas_gh90 k is the image of -4 by g ! I hope it's clear now !...

anonymous · Answer

yeah it is!thanks :)

anonymous · Answer

np :) ;)