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Confused

0
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The function $$f(x)$$ satisfies $$f(x) + f(x + 2y) = 6x + 6y - 8$$
for all real numbers $$x$$ and $$y$$ Find the value of $$x$$ such that $$f(x) = 0$$

Aug 22, 2019

#1
+791
+4

The function $$f(x)$$ satisfies $$f(x)+f(x+2y)\ =\ 6x+6y-8$$ or all real numbers $$x$$ and $$y$$ Find the value of $$x$$ such that $$f(x)\ =\ 0$$

$$f(x)+f(x+2y)=6x+6y-8$$

$$f(x)+2y\ =\ 6x+6y-8$$

$$f(x)\ =\ 6x+6y-8+2y$$

$$f(x)\ =\ 6x+8y-8$$

$$f(x)\ =\ 8y-8$$

$$f(x)\ =\ 1$$

If im wrong I'm sorry I did this in my head in like three minutes.

Aug 23, 2019
#2
+166
+3

Your answer was incorrect but helped me realize that the answer is 4/3. So in an indirect way you got the right result. Thank you for helping

Aug 23, 2019
#3
+791
+2

you are welcome

travisio  Aug 23, 2019
#4
+23273
+3

The function $$f(x)$$satisfies $$f(x) + f(x + 2y) = 6x + 6y - 8$$
for all real numbers $$x$$ and $$y$$
Find the value of $$x$$ such that $$f(x) = 0$$

$$\begin{array}{|rcll|} \hline \mathbf{f(x) + f(x + 2y)} &=& \mathbf{6x + 6y - 8} \quad &| \quad y= 0\\\\ f(x) + f(x + 2\cdot 0) &=& 6x + 6\cdot 0 - 8 \\ f(x) + f(x) &=& 6x - 8 \\ 2f(x)&=& 6x - 8 \quad &| \quad : 2 \\ f(x)&=& 3x - 4 \quad &| \quad f(x) = 0 \\ 0 &=& 3x - 4 \\ 3x &=& 4 \quad &| \quad : 3 \\ \mathbf{x} &=& \mathbf{\dfrac{4}{3}} \\ \hline \end{array}$$

Aug 23, 2019