Math Problem Statement
Two piecewise functions h(x) and g(x) are shown. What is the value of h(2) + g(1)?
Solution
The problem provides two piecewise functions and , and we are tasked with finding .
Step 1: Determine
The piecewise function for is defined as:
\begin{cases} -3x & \text{for } x < 2 \\ 4x + 1 & \text{for } x \geq 2 \end{cases}$$ Since $$x = 2$$, we use the second case $$4x + 1$$: $$h(2) = 4(2) + 1 = 8 + 1 = 9$$ ### Step 2: Determine $$g(1)$$ The piecewise function for $$g(x)$$ is defined as: $$g(x) = \begin{cases} x^2 + 2 & \text{for } x < 3 \\ x^3 & \text{for } x \geq 3 \end{cases}$$ Since $$x = 1$$, we use the first case $$x^2 + 2$$: $$g(1) = 1^2 + 2 = 1 + 2 = 3$$ ### Step 3: Add $$h(2)$$ and $$g(1)$$ Now, calculate $$h(2) + g(1)$$: $$h(2) + g(1) = 9 + 3 = 12$$ ### Final Answer: The value of $$h(2) + g(1)$$ is $$\boxed{12}$$ (Option C). --- Would you like any further explanation or details? Here are some related questions you might explore: 1. How do you evaluate a general piecewise function at a given point? 2. What is the significance of using piecewise functions in real-world modeling? 3. How do the behaviors of $$h(x)$$ and $$g(x)$$ differ as $$x$$ increases? 4. What are the conditions for continuity in piecewise functions like $$h(x)$$ and \(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
h(x) = {-3x \,\text{for} \, x < 2, \, 4x + 1 \,\text{for} \, x \geq 2}
g(x) = {x^2 + 2 \,\text{for} \, x < 3, \, x^3 \,\text{for} \, x \geq 3}
Theorems
-
Suitable Grade Level
Grades 9-12