Question 220553
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: {{{highlight_green(f(x) = 6x + 5)}}}


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