Calcmathlete
If f(x + 3) = \(x^2 + 2x + 4\), find f(x).
Do I just plug in x + 3 for x?



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waterineyes
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Replace x + 3 by x..
So put x  3..

Calcmathlete
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Wait, why would that work? I just want to understand the dynamics of why it works.

sai1234
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put x  3 inplace of x because f((x3)+3)=f(x3+3)=f(x)

waterineyes
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If you replace there x by x 3:
Then:
\[f(\color{green}{x} + 3) = f(\color{blue}{x  3} + 3) = f(x)\]

Calcmathlete
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Oh I get it now...
f(x) = x^2  4x + 7?

waterineyes
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Well Done..

Calcmathlete
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Thanks :)

waterineyes
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Hey right this time you became 93..
Congratulations..

Calcmathlete
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Thank you again :)