Question 220553: If f(x-2)=6x-7, what is f(x)?
The answer is f(x)=6x+5, but I have no idea how the answer is found! I keep ending up with 6x-17. Here is what I did....
f(x)= 6(x-2)+2-7
f(x)= 6x-12-5
f(x)= 6x-17
Please help! I think you're supposed to add 2 somewhere but I don't know where, why or how!
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If f(x-2)=6x-7, what is f(x)?
The answer is f(x)=6x+5
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The original equation was shifted 2 units to the right to get
f(x-2) = 6x-7
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So shift it 2 units to the left to get back to f(x)
f(x) = 6(x+2)-7
f(x) = 6x+12-7
f(x) = 6x+5
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Cheers,
Stan H.
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! If f(x - 2) = 6x 7, what is f(x)?
Since we need the right side of the equation in f(x 2) = 6x - 7 to contain the binomial (x 2), we have to fix it to make it that way.
Since we have 6x 7 on the right-hand side of the equation, and we need to the binomial (x 2), we then need to subtract 5, and then add 5 to the right side. In other words,
f(x - 2) = 6x 7 now becomes: f(x - 2) = 6x 7 5 + 5.
As seen, 5 was subtracted, and then added to the right-side to adjust but not change the equation.
Now, f(x - 2) = 6x 7 5 + 5 can be rewritten as: f(x - 2) = 6x 12 + 5, which can again be rewritten as f(x - 2) = 6(x 2) + 5.
Now, since f(x - 2) = 6(x 2) + 5, then f(x) = 6(x) + 5, or: 
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