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)

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:
$$F(x) =
\begin{cases}
x^2 & \text{if } x \le -3 \\
9 - x^2 & \text{if } -3 < x \le 3 \\
x^2 & \text{if } x > 3
\end{cases}$$
---
### **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:** $$F(-3) = (-3)^2 = 9$$
---
### **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:** $$F(3) = 9 - (3)^2$$
$$F(3) = 9 - 9 = 0$$
---
### **Summary of Results**
* **$f(-3) = 9$**
* **$f(3) = 0$**
RELATED QUESTIONS
For f(x) =-x^2-x+5 , find... (answered by jim_thompson5910)

for f(x)=-5x^2-4, find f(-3),and f(3) F(-3)=... (answered by Alan3354)

For f(x) = SqRt(x^3 + 1) find... (answered by jsmallt9)

f(x) = x^3 - 12x - 1 Find all values of x for the given function where the tangent... (answered by ewatrrr,Fombitz)

For the function f(x) = 3^x find... (answered by ikleyn)

For f(x)= 1/x^2-3 Find: a. f(3) b.... (answered by Alan3354)

For f(x)=9x-2, find... (answered by solver91311)

For f(x)= -5x + 3 . Find... (answered by jim_thompson5910)

Find an equation for line with y-intercept 3 that is perpendicular to the line... (answered by Edwin McCravy)