Recent questions tagged functions

Problem: In how many ways can 2n seats in a congress be divided among 3 parties so that the coalition of any 2 parties will ensure them of majority?Answer: Total number o...

Let $f(x) = x – [x],$ where $x\geq 0$ and $[x]$ is the greatest integer not larger than $x.$ Then $f(x)$ is a monotonically increasing function monotonically decreasing f...

A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)...

If $f\left(x+\frac{y}{8}, x-\frac{y}{8}\right)=xy$, then $f(m, n)+f(n, m)=0$Only when $m=n$Only when $m ≠ n$Only when $m= -n$For all $m$ and $n$

Let $f: [0, 1]\rightarrow \mathbb{R}$ be a fixed continuous function such that $f$ is differentiable on $(0, 1)$ and $f(0) = f(1) = 0$. Then the equation $f(x) = f' (x)$ ...

Let $m \leq n$ be natural numbers. The number of injective maps from a set of cardinality m to a set of cardinality $n$ is $m!$$n!$ $(n − m)!$ None of the above

Let $k$ be an integer at least $4$ and let $\left[k\right]= \left\{1, 2,...,k\right\}$. Let $f:\left[k\right]^{4}\rightarrow \left\{0, 1\right\}$ be defined as follows: $...

Consider a function $T_{k, n}: \left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ which returns $1$ if at least $k$ of its $n$ inputs are $1$. Formally, $T_{k, n}(x)...

For $x, y\in \left\{0, 1\right\}^{n}$, let $x ⊕ y$ be the element of $\left\{0, 1\right\}^{n}$ obtained by the component-wise exclusive-or of $x$ and $y$. A Boolean funct...

If $f,g:\mathbb{R}\rightarrow \mathbb{R}$ are uniformly continuous functions, then their compositions g ∘ f is.Uniformly continuousContinuous but not uniformly continuous...

Let $f$ be an one to one function from the closed interval [0, 1] to the set of real numbers $R$, then.$f$ must be ontoRange of $f$ must contain a rational numberRange of...