Suppose f:R rightarrow R where f(x)=⌊x/2⌋, if T={3,4,5} , then what's the inverse of f(T)?

Mutignaniz2

Mutignaniz2

Answered question

2022-09-07

How to solve for the inverse of f for a floor function? I really need to learn the method.
I was doing some exercises on discrete maths and came across this question I don't know how to solve, nor can I find any relevant examples in my book.
Suppose f : R R where f ( x ) = x / 2 , if T = { 3 , 4 , 5 } , then what's the inverse of f(T)?
I know how to get f(T) but how to get its inverse? Could anyone teach me please?

Answer & Explanation

Theodore Dyer

Theodore Dyer

Beginner2022-09-08Added 10 answers

Step 1
f : R R x x 2
Before we start trying to solve equations, let's try to see a pattern. I looked for a few of the largest intervals that get sent into a few integers.
[ 0 , 2 ) 0 [ 2 , 4 ) 1 [ 4 , 6 ) 2
Step 2
It seems that, for n Z + , f 1 ( { n } ) = [ 2 n , 2 n + 2 )

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Discrete math

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?