If f(x)=3 x^4-5 x^2+7, find f(x-1). - Vidyadip

Question

If $f(x)=3 x^4-5 x^2+7$, find $f(x-1)$.

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Answer

$ f(x)=3 x^4-5 x^2+7$
$\therefore f(x-1)=3(x-1)^4-5(x-1)^2+7$
$=3\left(x^4-{ }^4 C_1 x^3+{ }^4 C_2 x^2-{ }^4 C_3 x+{ }^4 C_4\right)-5\left(x^2-2 x+1\right)+7$
$=3\left(x^4-4 x^3+6 x^2-4 x+1\right)-5\left(x^2-2 x+1\right)+7$
$=3 x^4-12 x^3+18 x^2-12 x+3-5 x^2+10 x-5+7$
$=3 x^4-12 x^3+13 x^2-2 x+5 $

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