Math Problem Statement
What is the value of f(-5) in the piecewise function f(x) = { -3x + 1, when x > 1; -2x, when x = 1; 2x - 1, when x < 1 }?
Solution
The problem is asking for the value of in the given piecewise function:
\begin{cases} -3x + 1 & \text{when } x > 1 \\ -2x & \text{when } x = 1 \\ 2x - 1 & \text{when } x < 1 \end{cases}$$ Since $$x = -5$$, and $$-5 < 1$$, we use the third piece of the function: $$f(x) = 2x - 1 \quad \text{for} \quad x < 1.$$ Substitute $$x = -5$$: $$f(-5) = 2(-5) - 1 = -10 - 1 = -11.$$ Thus, $$f(-5) = -11$$. The correct answer is $$-11$$. Would you like further details or have any questions? Here are 5 related questions: 1. What is the value of $$f(2)$$ in this piecewise function? 2. How do you determine which piece of the function to use for $$f(x)$$? 3. What is the value of $$f(1)$$? 4. How would you graph this piecewise function? 5. What would happen if $$x = 0$$ in the piecewise function? **Tip**: Always check the domain conditions before evaluating a piecewise function.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = 2x - 1 when x < 1
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 9-12