SOLUTION: Determine f(x) if f(x+2) – f(x-3)=20 and the point (-2, 6) lies on the line
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Question 187097: Determine f(x) if f(x+2) – f(x-3)=20 and the point (-2, 6) lies on the line
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The first thing to realize is that if f( x ) were non-linear, then:
 – f(x-3))
would be some function of x rather than a constant. Hence f( x ) is linear.
Given that, we can use the point-slope form of the equation of a line to derive an equation for the line.
 )
 = y = mx + 2m + 6)
So:
 = m(x+2) + 2m + 6 = mx + 4m + 6 )
And:
 = m(x-3) + 2m + 6 = mx - m + 6)
And then:
 – f(x-3) = (mx + 4m + 6) - (mx - m + 6) = 5m = 20)
So:
Now:
 = 4x + 8 + 6 = 4x + 14)
Check the answer:
 = 4(-2) + 14 = 6)
 = 4(x + 2) + 14 = 4x + 22)
 = 4(x - 3) + 14 = 4x + 2)
and 22 - 2 = 20.
John
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