Alan

Answered here: https://web2.0calc.com/questions/probability-question_35#r5

x = 2, y = -3/2 

Long division:

The line through (7,8) and (9,0) can be written as y = mx + c, where m and c are constants found from the following:

8 = 7m + c

0 = 9m + c

Hence 2m = -8 or m = -4, so c = 8 + 7*4 = 36

Therefore the line is described by  y = -4x + 36

Now equate this and y = 2x - 10 to find the values of x (=a) and y (=b) that satisfy both equations.

\(\lambda\) is the Greek letter lambda.

As follows:

This graph should help (always supposing it's visible!):

You are trying to find functions that satisfy the relationship:  g(x)*g(y) = g(x+y) + x*y

Pretend I defined the function as  g(z) = z + 1.

When z = x we have  g(x) = x+1

When z = y we have  g(y) = y + 1

When z = x+y we have g(x+y) = x + y + 1

So this definition of the function g satisfies the specified criterion.

I suspect its the only one, but I haven't attempted to prove it!

Scroll down the page labelled Answers.  You can see it there.

Hmm, not quite!  if you let x go to infinity then you get 0 = 0.

Let x go to 0 is fine.  Probably better to let x go to 1 rather than infinity for another choice though.