Math Problem Statement
Solution
The task in the image involves calculating values for different mathematical functions and determining whether each function is odd, even, or neither. Let's solve the functions for the given values of and then determine the nature of each function.
1. Polynomial Function:
Calculations:
- For
2. Trigonometric Function:
Calculations:
- For
3. Cubic Function:
Calculations:
- For
Nature Determination:
- Odd Function:
- Even Function:
Let's compute the necessary values and determine the nature of these functions.Here are the calculated values for each function:
1. Polynomial Function:
- For , the values of are respectively.
2. Trigonometric Function: ( f(x) = 4\sin(x)
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Math Problem Analysis
Mathematical Concepts
Functions
Odd and Even Functions
Trigonometry
Polynomials
Formulas
f(-x) = -f(x) (Odd Function Definition)
f(-x) = f(x) (Even Function Definition)
Quadratic function f(x) = 2x^2 + 3
Trigonometric function f(x) = 4sin(x) + 1
Cubic function f(x) = 2x^5 + 3x
Theorems
Odd and Even Function Theorem
Suitable Grade Level
Grades 10-12
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