Question

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

Answer 1

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.