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The function f(x)=2/3x-4 was replaced with f(x+k)=2/3x-6 what is the value of k

User Vlee
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Answer:

The given function
f(x)=(2x)/(3)-4 was replaced with
f(x+k)=(2x)/(3)-6 then the value of k is -3

that is k=-3.

Explanation:

The given function is
f(x)=(2x)/(3)-4\hfill (1)

and when x=x+k then
f(x+k)=(2x)/(3)-6\hfill (2)

Now to find the value of k:

Put x=x+k in the function f(x)


f(x)=(2x)/(3)-4


f(x+k)=(2(x+k))/(3)-4


f(x+k)=(2x+2k)/(3)-4\hfill (3)

Now comparing equations (2) and (3) we get


f(x+k)=(2x+2k)/(3)-4=(2x)/(3)-6


(2x+2k)/(3)-4=(2x)/(3)-6


(2x+2k)/(3)-4-(2x)/(3)+6=0


(2x)/(3)+(2k)/(3)-4-(2x)/(3)+6=0


(2k)/(3)+2=0


(2k)/(3)=-2


k=(-2* 3)/(2)


k=-3

Therefore k=-3

Therefore the given function
f(x)=(2x)/(3)-4 was replaced with
f(x+k)=(2x)/(3)-6 then the value of k is -3

that is k=-3.

User Logan Koester
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