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.

Answer 1

x=0 is the only answer I think!

Answer 2

how ? .. can you solve ?

Answer 3

yes

Answer 4

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

Answer 5

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

Answer 6

@mas_gh90 Sorry but, you made a mistake !

Answer 7

thanks!can u explain more?

Answer 8

first , the question is to find k not x.

Answer 9

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

Answer 10

yeah it is!thanks :)

Answer 11

np :) ;)