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QuestionFind f(x−1)f(x-1) if f(x)=x2−1f(x)=x^{2}-1. Choose the correct option: a) x2−2x^{2}-2, b) x2−2x−2x^{2}-2 x-2, c) x2−xx^{2}-x, d) x2−2xx^{2}-2 x, e) x2x^{2}.

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x) is defined as f(x)=x−1f(x)=x^{}-1. . We need to find the value of f(x−1)f(x-1).

STEP 2

To find the value of f(x−1)f(x-1), we need to replace every instance of xx in the function f(x)f(x) with (x−1)(x-1).
f(x−1)=(x−1)2−1f(x-1)=(x-1)^{2}-1

STEP 3

Expand the square in the equation.
(x−1)2=x2−2x+1(x-1)^{2}=x^{2}-2x+1So,f(x−1)=x2−2x+1−1f(x-1)=x^{2}-2x+1-1

STEP 4

implify the equation by combining like terms.
f(x−1)=x2−2xf(x-1)=x^{2}-2xSo, the correct answer is option d) x2−2xx^{2}-2x.

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