Math Problem Statement
Suppose 𝑆={0,1,2,3,4,5,6,7,8,9,10,11}S={0,1,2,3,4,5,6,7,8,9,10,11} and that the function 𝑓:𝑆→𝑆f:S→S is given by:
𝑓(𝑥)=(10𝑥2+7𝑥+4)mod12f(x)=(10x2+7x+4)mod12.
Let 𝑇={0,7}T={0,7}.
Recall that the Numbas syntax for the set {𝑎,𝑏,𝑐}{a,b,c} is set(a,b,c)
.
a)
What is 𝑓(𝑇)f(T)?
Solution
We are given the function defined as:
We are also given the set . Our goal is to compute , which means finding the values of for .
Step 1: Compute
For :
Step 2: Compute
For : First, compute the values inside the parentheses: Now compute the modulo operation:
Step 3: Combine results
Now that we have and , we can write the set as:
So, the result is:
Do you want more details or have any questions?
Here are 5 related questions you can consider:
- What is for ?
- How would the set change if ?
- Can you generalize for any modulo 12?
- How does the choice of modulo (e.g., mod 12 vs. mod 5) affect the results of ?
- What if the polynomial were cubic instead of quadratic?
Tip: When computing functions with modular arithmetic, it's often easier to simplify intermediate steps modulo the given number.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Modular Arithmetic
Quadratic Functions
Formulas
f(x) = (10x^2 + 7x + 4) mod 12
Theorems
Modulo Operation
Polynomial Function Evaluation
Suitable Grade Level
Grades 9-12