Math Problem Statement
WH2_M1151_AU24.pdf
148.91 KB
in part g) ii) evaluate g(1)
Solution
The function is given as a piecewise function:
\begin{cases} x^2 - 6x + 13 & \text{if } x \geq 1 \\ 2\sqrt{2 - x} & \text{if } x < 1 \end{cases}$$ To evaluate $$g(1)$$, we use the first piece of the piecewise function, since $$g(x) = x^2 - 6x + 13$$ for $$x \geq 1$$. Substituting $$x = 1$$: $$g(1) = 1^2 - 6(1) + 13 = 1 - 6 + 13 = 8$$ Thus, $$g(1) = 8$$. Would you like any more details on this, or have other questions? Here are five related questions to expand on this concept: 1. How do you evaluate a derivative using the limit definition for piecewise functions? 2. How do you check if a piecewise function is continuous at a given point? 3. What does the existence of a tangent line at a point tell you about the function's behavior? 4. How do one-sided limits help in determining the differentiability of a function? 5. Can you describe a situation where a function has a jump discontinuity? **Tip:** When dealing with piecewise functions, always ensure you're using the correct "piece" of the function for the interval you're evaluating.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Evaluation of Functions
Continuity
Formulas
g(x) = x^2 - 6x + 13 for x >= 1
g(x) = 2√(2 - x) for x < 1
Theorems
Continuity of Piecewise Functions
Limit Definition of Derivatives
Suitable Grade Level
University Level (Calculus I)