Piecewise Function f(x) = 5/x for x > 5 and x

Math Problem Statement

f(x) = \begin{cases} \dfrac{5}{x} & \text{for} ~~~~x\gt{5} \ x-4& \text{for} ~~~~ x \leq5\end{cases}

The given function is a piecewise function, which is defined as:

\begin{cases} \dfrac{5}{x} & \text{for } x > 5 \\ x - 4 & \text{for } x \leq 5 \end{cases}$$ This means that the value of $$f(x)$$ depends on the value of $$x$$. Specifically: - For $$x > 5$$, the function follows the expression $$f(x) = \dfrac{5}{x}$$. - For $$x \leq 5$$, the function follows the expression $$f(x) = x - 4$$. If you have a specific question regarding this function (e.g., evaluating it at a particular value, finding limits, or analyzing continuity), feel free to ask! ### Do you want any further details or clarifications? Here are some related questions: 1. What is the value of $$f(6)$$? 2. Is this function continuous at $$x = 5$$? 3. What happens to $$f(x)$$ as $$x$$ approaches 5 from the right? 4. How would you graph this function? 5. What is the domain and range of this piecewise function? **Tip:** When working with piecewise functions, always check the behavior at the transition points (in this case, $$x = 5$$) to ensure continuity and correct interpretation.

Drop file here or Click Here to upload

Piecewise Functions
Continuity
Limits

f(x) = 5/x for x > 5
f(x) = x - 4 for x ≤ 5

Piecewise function definition
Continuity at a point
Limit of a function

Grades 9-12

Analysis of Piecewise Function with Continuity Check at x = 2

Piecewise Function Evaluation: Find f(7)

Analyzing a Piecewise Function with Continuity and Limits

Piecewise Function f(x): 2x + 1 for x < 0 and 2x + 2 for x ≥ 0

Understanding Piecewise Functions: f(x) = -x + 5 for x < 2, f(x) = x - 4 for x >= 2