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Question 1079641: if f(x-1) = x² -4x+8, then f(x+2) is equal to
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! We want to go from "x-1" to "x+2". To make the jump, we need to add on 3 (since 3+(-1) = 2)
In other words, if we add on 3 to (x-1), then we get (x-1)+3 = x-1+3 = x+2 which is the desired expression we want.
To achieve this goal, we can replace every copy of x with x+3 as shown below in step 4. Take note the color coding connection between steps 3 and 4, specifically what is replaced. After the substitution is made, we can simplify
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g(x) = f(x-1) = x^2 - 4x + 8
g(x) = f( (x)-1 ) = (x)^2 - 4(x) + 8
g(x) = f( (x)-1 ) = (x)^2 - 4(x) + 8
g(x+3) = f( (x+3)-1 ) = (x+3)^2 - 4(x+3) + 8
g(x+3) = f( x+2 ) = (x+3)^2 - 4(x+3) + 8
g(x+3) = f( x+2 ) = 1(x^2+6x+9) - 4(x+3) + 8
g(x+3) = f( x+2 ) = x^2+6x+9 - 4x-12 + 8
g(x+3) = f( x+2 ) = x^2+6x - 4x+9-12 + 8
g(x+3) = f( x+2 ) = x^2+2x+5
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Final Answer: x^2+2x+5
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