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bezimeni [28]
3 years ago
7

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

Mathematics
1 answer:
HACTEHA [7]3 years ago
7 0

Answer:

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

that is k=-3.

Step-by-step explanation:

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

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

Now to find the value of k:

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

f(x)=\frac{2x}{3}-4

f(x+k)=\frac{2(x+k)}{3}-4

f(x+k)=\frac{2x+2k}{3}-4\hfill (3)

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

f(x+k)=\frac{2x+2k}{3}-4=\frac{2x}{3}-6

\frac{2x+2k}{3}-4=\frac{2x}{3}-6

\frac{2x+2k}{3}-4-\frac{2x}{3}+6=0

\frac{2x}{3}+\frac{2k}{3}-4-\frac{2x}{3}+6=0

\frac{2k}{3}+2=0

\frac{2k}{3}=-2

k=\frac{-2\times 3}{2}

k=-3

Therefore k=-3

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

that is k=-3.

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