Math Problem Statement
f(x)={
(x−2)
2
−9
6
for x
=4
1
1
for x=4
1
1
Find , f, of, 4
Find f(4)
Solution
To find , let's examine the function definition.
The function is defined as:
\begin{cases} \frac{(x-2)^2 - 9}{6} & \text{for } x \neq 4 \\ \frac{1}{11} & \text{for } x = 4 \end{cases}$$ Since we need to find $$f(4)$$, we apply the rule for when $$x = 4$$: $$f(4) = \frac{1}{11}$$ So, the answer is: $$f(4) = \frac{1}{11}$$ Would you like more details on this, or do you have any further questions? Here are some related questions for further practice: 1. How would you find $$f(x)$$ for values of $$x \neq 4$$? 2. Can you simplify the expression $$\frac{(x-2)^2 - 9}{6}$$? 3. What is the limit of $$f(x)$$ as $$x$$ approaches 4? 4. How would the function change if $$f(4)$$ were defined differently? 5. What is the derivative of $$f(x)$$ for $$x \neq 4$$? **Tip:** Piecewise functions are defined with different expressions based on the value of $$x$$; pay careful attention to which part of the definition applies to the value you’re given.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = (x-2)^2 - 9 / 6 for x ≠ 4
f(x) = 1/11 for x = 4
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 9-11