Discrete Math: Functions with Powers

In summary, the homework problem is to prove that for all m,n ε N, f^m*f^n = f^(m+n) for a function f from A to A. The attempted solution involved using the property a^m * a^n = a^(m+n) and resulted in the incorrect step of f(f^m * f^n) instead of f(f^(m+n)).
  • #1
finalsblow
2
0
Did this as a homework problem, got it wrong obviously. Not too sure how to solve it otherwise

Homework Statement


Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+N)


Homework Equations





The Attempt at a Solution



f^(m+1) f^(n+1) = f(f^m) * f(f^n)
= f(f^m * f^n) <--- this I think is what I did wrong
= f(f^(m+n)) since a^m * a^n = a^(m+n)
= f^(m+n+1)
= f^(x+1) where x = m+n
 
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  • #2
Can't find edit button:
Found an error.. it should say
1. Homework Statement
Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+n)
 

Related to Discrete Math: Functions with Powers

1. What is a function with powers in discrete math?

A function with powers in discrete math is a type of mathematical function that involves raising a variable to a certain power. This power can be a positive integer, negative integer, or a fraction. The function can also have multiple powers and different variables.

2. How do you graph a function with powers in discrete math?

To graph a function with powers in discrete math, you can use a table of values to plot points and then connect them with a line. You can also use a graphing calculator or an online graphing tool to plot the function. Remember to label the axes and include any restrictions or asymptotes in the graph.

3. What are the domain and range of a function with powers in discrete math?

The domain of a function with powers is the set of all possible input values or independent variables. The range is the set of all possible output values or dependent variables. In a function with powers, the domain can be restricted by the powers or the type of variable, while the range can be any real number depending on the powers and coefficients in the function.

4. How do you find the inverse of a function with powers in discrete math?

To find the inverse of a function with powers in discrete math, you can follow the steps for finding the inverse of any function. First, switch the positions of the x and y variables. Then, solve for y and replace it with f^-1(x). Finally, simplify the expression and state the domain and range of the inverse function.

5. How is a function with powers used in real life?

A function with powers can be used in many real-life applications, such as in physics, engineering, and economics. For example, in physics, the position of a moving object can be described using a quadratic function with powers. In economics, the demand and supply of a product can be modeled using an exponential function with powers. In general, functions with powers are used to model relationships between quantities that change over time or in response to other variables.

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