SOLUTION: F(x)= {x^2 for <(with line underneath< )-3 9-x^2 for -3< x < ( with line underneath<) 3 X^2 for x>3 Find f(-3) Find f(3)

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Question 1164583: F(x)= {x^2 for <(with line underneath< )-3
9-x^2 for -3< x < ( with line underneath<) 3
X^2 for x>3
Find f(-3)
Find f(3)

Answer by CPhill(2264) (Show Source):
You can put this solution on YOUR website!
To find the values of the piecewise function $F(x)$ at specific points, we must identify which interval the given $x$-value falls into and use the corresponding formula.
The function is defined as:
$$F(x) =
\begin{cases}
x^2 & \text{if } x \le -3 \\
9 - x^2 & \text{if } -3 < x \le 3 \\
x^2 & \text{if } x > 3
\end{cases}$$
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### **1. Find $f(-3)$**
* **Identify the interval:** We look for the condition that includes $-3$. The first part of the function is defined for $x \le -3$ ("less than or equal to").
* **Apply the formula:** $F(x) = x^2$
* **Calculation:** $$F(-3) = (-3)^2 = 9$$
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### **2. Find $f(3)$**
* **Identify the interval:** We look for the condition that includes $3$. The middle part of the function is defined for $-3 < x \le 3$ ("greater than $-3$ and less than or equal to $3$").
* **Apply the formula:** $F(x) = 9 - x^2$
* **Calculation:** $$F(3) = 9 - (3)^2$$
$$F(3) = 9 - 9 = 0$$
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### **Summary of Results**
* **$f(-3) = 9$**
* **$f(3) = 0$**