Question 1180555: Greetings,
I am having troubles solving this question and confused on how to start: If f (x1, x2) = a + bx1 + cx2 + dx1x2, what is f (x1 + k, x2) - f (x1, x2)?
Do i just plug in x1 + k every time I see x1 for the first part?
If you could provide the solution and a brief explanation thank you!
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Yes you are correct. You'll replace every x1 with x1+k to find that,
f(x1, x2) = a + b*x1 + c*x2 + d*x1*x2
f(x1+k, x2) = a + b*(x1+k) + c*x2 + d*(x1+k)*x2
f(x1+k, x2) = a + b*x1+b*k + c*x2 + d*x1*x2+d*k*x2
Then we subtract off f(x1,x2) from both sides
You should find that the following terms cancel- a and -a
- b*x1 and -b*x1
- c*x2 and -c*x2
- d*x1*x2 and -d*x1*x2
In short, everything of f(x1, x2) = a + b*x1 + c*x2 + d*x1*x2 cancels out due to subtraction
So,
f(x1+k, x2) - f(x1,x2) = a + b*x1+b*k + c*x2 + d*x1*x2+d*k*x2 - f(x1,x2)
f(x1+k, x2) - f(x1,x2) = a + b*x1+b*k + c*x2 + d*x1*x2+d*k*x2 - (a + b*x1 + c*x2 + d*x1*x2)
f(x1+k, x2) - f(x1,x2) = a + b*x1+b*k + c*x2 + d*x1*x2 + d*k*x2 - a - b*x1 - c*x2 - d*x1*x2
f(x1+k, x2) - f(x1,x2) = b*k+d*k*x2
Answer: b*k+d*k*x2
You can factor this into (b+d*x2)*k
Be sure not to mix up x2 with x^2
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