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

25%=1/4=40100%=4/4=?4times40=160He allocated $160 each month...

The function f(x)=2/3x-4 was replaced with f(x+k)=2/3x-6

Tariah5970

14.01.2022

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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