QuestionSimplify $f(x-3)$ for the function $f(x)=x^{2}-2$ . What is $f(x-3)=?$

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x)=x^{}-$ . We need to find and simplify the expression $f(x-3)$

STEP 2

To find $f(x-)$ , we substitute $x-$ into the function $f(x)$ .
$f(x-) = (x-)^{2}-2$

STEP 3

Now, we expand the square in the equation.
$(x-3)^{2} = x^{2} -6x +9$ So, the equation becomes $f(x-3) = x^{2} -6x +9 -2$

STEP 4

Finally, we simplify the equation by combining like terms.
$f(x-3) = x^{2} -6x +7$ So, the simplified expression for $f(x-3)$ is $x^{2} -6x +7$ .

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