Math Problem Statement
ind f ( 8 ) f(8), where f ( x ) f(x) is the following piecewise function.
f ( x )
{ 3 x 2 if x < − 1 5 x − 4 if − 1 < x < 3 x + 1 if 3 < x
f(x)= ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧
3x 2
5x−4 x+1
if x<−1 if −1<x<3 if 3<x
Solution
To find , we need to determine which part of the piecewise function applies when .
The given piecewise function is:
\begin{cases} 3x^2 & \text{if } x < -1, \\ 5x - 4 & \text{if } -1 < x < 3, \\ x + 1 & \text{if } 3 < x. \end{cases}$$ Since $$8 > 3$$, the third case $$f(x) = x + 1$$ applies. ### Substitute $$x = 8$$ into the third case: $$f(8) = 8 + 1 = 9.$$ ### Final Answer: $$f(8) = 9.$$ --- Would you like a detailed breakdown of piecewise functions or their graphing? Here are 5 related questions to explore: 1. How do we determine which piece of a piecewise function to use for a given $$x$$? 2. Can you show me how to graph a piecewise function like this one? 3. What happens at the boundaries of the pieces in a piecewise function? 4. How would $$f(x)$$ change if there were equalities (e.g., $$x \leq -1$$)? 5. Could you explain continuity and discontinuity in piecewise functions? **Tip:** Always double-check the conditions in a piecewise function, especially at boundary points, to avoid confusion about which case applies.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution in Functions
Formulas
f(x) = 3x^2
f(x) = 5x - 4
f(x) = x + 1
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 9-12