Math Problem Statement

f(x)={ −(x+6) 2

−3 ​

for x  =−5 1 1 ​

for x=−5 1 1 ​

Find , f, of, minus, 5 Find f(−5)

Solution

It seems like you're asking to find f(5)f(-5) for the piecewise function f(x)f(x).

From the given function:

\begin{cases} -(x+6)^2 - 3 & \text{for } x \neq -5 \\ 1 & \text{for } x = -5 \end{cases}$$ We are asked to find $$f(-5)$$. Since the function has a specific definition for $$x = -5$$, we use the second part of the piecewise function: $$f(-5) = 1$$ Therefore, $$f(-5) = 1$$. --- Would you like more details on piecewise functions or any other explanation? Here are some related questions for further exploration: 1. How do piecewise functions work and why are they useful? 2. What is the limit of a piecewise function as $$x$$ approaches a specific value? 3. How would you graph the given piecewise function? 4. Can piecewise functions be continuous? Under what conditions? 5. What is the difference between a piecewise linear function and a quadratic one? Tip: Always pay close attention to the specific conditions given for each piece of a piecewise function!

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Substitution in Functions

Formulas

f(x) = { -(x+6)^2 - 3 for x ≠ -5, 1 for x = -5

Theorems

Definition of Piecewise Functions

Suitable Grade Level

Grades 9-10