f(x)=(x-1)³ = x³ -3x² +3x -1 **f(x+1) = (x+1-1)**³ = x ³
f ( x + 1 ) = ( x + 1 ) 3 − 3 ( x + 1 ) 2 + 3 ( x + 1 ) − 1 f ( x + 1 ) = x 3 + 3 x 2 + 3 x + 1 − 3 ( x 2 + 2 x + 1 ) + 3 x + 3 − 1 f ( x + 1 ) = x 3 + 3 x 2 + 6 x + 3 − 3 x 2 − 6 x − 3 f ( x + 1 ) = x 3 ⇒ C
To find f ( x + 1 ) for the function f ( x ) = x 3 − 3 x 2 + 3 x − 1 , substitute x + 1 into the function and simplify. The result is f ( x + 1 ) = x 3 , making option C the correct choice. The calculation involves expanding, combining like terms, and simplifying the expression.
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