If $f (x) = x^{2} + x + 1$ find $f (x - 1)$

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Solution

$f (x) = x^{2} + x + 1$
Now
$f (x - 1) = (x - 1)^{2} + (x - 1) + 1$
$= x^{2} + 1 - 2 x + x - 1 + 1$
$= x^{2} - 2 x + x + 1$
$= x^{2} - x + 1$

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