Recent questions tagged goclasses-cs-dpp-day-264

Let $X,Y,Z$ be finite sets with $|X|=6$, $|Y|=8$, and $|Z|=6$. Suppose $f:X\to Y$ and $g:Y\to Z$ are functions such that $g\circ f:X\to Z$ is bijective. Which of the foll...

Let $f,g,h:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=x^2+1$, $g(x)=2x-1$, and $h(x)=x^2-4$. Find $h\circ(g\circ f)$ and $(h\circ g)\circ f$.$4x^4+4x^2-3$ and $4x^4+4x^...

Consider the function $f:\mathbb{N}\to\mathbb{N}$ given recursively by $f(0)=2$ and $f(n+1)=2f(n)+n+1$ for every $n\ge0$. Find $f(5)$.

Let $S=\{0,1,2,3,4,5,6\}$. Each of the following defines a function from $S$ to $S$. Which function is both injective and surjective?$f(x)=(2x+1)\bmod 7$ $f(x)=x^2\bmod 7...

Let $f$ and $g$ be functions from the set of integers to the set of integers defined by $f(x)=2x+1$ and $g(x)=x^2-2$. Find the integer value of $x$ for which $(f\circ g)(...

Find the minimum value of $f(x,y)=xy+x+y$ subject to $x^2+y^2=1$.$-1$ $-\sqrt{2}$ $-1/2$ $-2$

Choose the largest interval of $x$ on which the function $f(x)=x^2\ln x$, where $x>0$, is convex.$(0,e^{-3/2})$ $[e^{-3/2},\infty)$ $(0,\infty)$ $[e^{-1},\infty)$

A company splits $12$ research hours between two tasks. If $x$ hours are spent on task A, then $12-x$ hours are spent on task B. The total difficulty score is $D(x)=x^2+(...

A research team has $60$ hours to divide between technical validation and market validation. If $x$ hours are spent on technical validation, then $60-x$ hours are spent o...

A company models its total production cost by $C(x)=x^2+\frac{16}{x}$, where $x>0$ is the number of units produced in hundreds. Find the minimum possible value of $C(x)$.