Find a function $H$ such that $H(H(x)) = H(x)$ for all numbers $x$, and such that $H(1)=36$, $H(2)=\pi/3$, $H(13)=47$, $H(36)=36$, $H(\pi/3)=\pi/3$, $H(47)=47$.
Any hints would be appreciated
2026-03-28 01:26:09.1774661169
Finding a function with some requirements
29 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in FUNCTIONS
- Functions - confusion regarding properties, as per example in wiki
- Composition of functions - properties
- Finding Range from Domain
- Why is surjectivity defined using $\exists$ rather than $\exists !$
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Lower bound of bounded functions.
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Given a function, prove that it's injective
- Surjective function proof
- How to find image of a function
Related Questions in FUNCTION-AND-RELATION-COMPOSITION
- Proof verifications: Elementary composition proofs. (if $g\circ f$ is one-to-one, then show $f$ is one-to-one etc.)
- Easy looking functional equation.
- Find matrix associated to linear transformation
- Inverse of a map $T_{(p,q)}(X \times Y) \to T_p X \times T_p Y$
- Prove that composition functions are surjective
- Function Composition Formulas
- Residue of composite functions
- Are there functions (or category of functions) that satisfy following conditions?
- How many successive logs until a number becomes $1$?
- What numbers can be created by $1-x^2$ and $x/2$?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Well, since you don't even require continuity, here's the minimal example: $$ H(x) = \begin{cases} 36, &x=1 \text{ or } 36 ,\\ \pi/3 , &x= 2 \text{ or } \pi/3, \\ 47 , &x=13 \text{ or } 47 \\ 0 &\text{else.} \end{cases} $$ You can easily check that $H(H(x)) = H(x)$ for any $x$ and it satisfies the other conditions trivially.