Question 1209949
.
The function f : R --> R satisfies
f(x)*f(y) - f(xy) = -2x - 6y + 10
for all x, y in R. Find f(x). 
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        In his post,  @CPhill derived the formula   f(x) = 2x+10   and states/claims that it is the solution to the problem.


        In this my post,  I will disprove his statement and will show that   f(x) = 2x+10   DOES  NOT  satisfy

        the given equation.



<pre>
To check, let's take  x= 2, y= 2.

Then f(2) = 2*2+10 = 14;

so  f(x)*f(y) = f(2)*f(2) = 14*14 = 196,

    f(xy) = f(2*2) = f(4) = 2*4+10 = 18.


Therefore, the left side of the basic equation is

    f(x)*f(y) - f(xy) = 14*14 - 18 = 196 - 18 = 178.    (Left side)


The right side of the basic equation is

    -2x - 6y + 10 = -2*2 - 6*2 + 10 = -4 - 12 + 10 = -16 + 10 = -6.    (Right side)


As you see from these calculations, the left side is not equal to the right side.
</pre>

<H3>The conclusion is: the "solution" by @CPhill is a FAKE.</H3>

Instead of to be a solution, it is an outright gibberish.