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Q.
If $f(x + 1) = x^2 - 3x + 2$, then f (x) is equal to:
Relations and Functions
Solution:
Given function is :
$f (x + 1) = x^2 - 3x + 2$
This function is valid for all real values of x.
So, putting x - 1 in place of x, we get
$f (x) = f (x - 1 + 1)$
$\Rightarrow \, f (x) = (x - 1)^2 - 3(x - 1) + 2$
$\Rightarrow \, f (x) = x^2 - 2x + 1 - 3x + 3 + 2$
$f (x) = x^2 - 5x + 6$