Math  /  Algebra

QuestionIf f(x)f(x) is defined as follows, find (a) f(3)f(-3), (b) f(0)f(0), and (c) f(3)f(3). f(x)={x2 if x<03 if x=02x+2 if x>0f(x)=\left\{\begin{array}{ll} x^{2} & \text { if } x<0 \\ 3 & \text { if } x=0 \\ 2 x+2 & \text { if } x>0 \end{array}\right. (a) f(3)=f(-3)= \square (Simplify your answer.)

Studdy Solution

STEP 1

1. The function f(x) f(x) is defined piecewise with three cases.
2. We need to evaluate f(x) f(x) for specific values: x=3 x = -3 , x=0 x = 0 , and x=3 x = 3 .

STEP 2

1. Determine which piece of the piecewise function applies for x=3 x = -3 and evaluate.
2. Determine which piece of the piecewise function applies for x=0 x = 0 and evaluate.
3. Determine which piece of the piecewise function applies for x=3 x = 3 and evaluate.

STEP 3

For x=3 x = -3 , identify the applicable piece of the function:
Since x<0 x < 0 , use f(x)=x2 f(x) = x^2 .

STEP 4

Evaluate f(3) f(-3) :
f(3)=(3)2 f(-3) = (-3)^2

STEP 5

Simplify the expression:
f(3)=9 f(-3) = 9
The value of f(3) f(-3) is:
9 \boxed{9}

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