Given the function $f(x) = 2x^2 - 3x + 7$ with domain {$-2, -1, 3, 4$}, what is the largest integer in the range of $f$?
The domain of the function $f(x)=\log_{\frac12}(\log_4(\log_{\frac14}(\log_{16}(\log_{\frac1{16}}x))))$ is an interval of length $\tfrac mn$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?
Suppose that $f(x+3)=3x^2 + 7x + 4$ and $f(x)=ax^2 + bx + c$. What is $a+b+c$?
A function $f$ has domain $[0,2]$ and range $[0,1]$. (The notation $[a,b]$ denotes $\{x:a \le x \le b \}$.) What are the domain and range, respectively, of the function $g$ defined by $g(x)=1-f(x+1)$?
Let $a > 0$, and let $P(x)$ be a polynomial with integer coefficients such that
$P(1) = P(3) = P(5) = P(7) = a$, and
$P(2) = P(4) = P(6) = P(8) = -a$.
What is the smallest possible value of $a$?
Find all polynomials $f(x)$ such that $f(x^2) = f(x)f(x+1)$.
Let $x, y \in [-\frac{\pi}{4}, \frac{\pi}{4}], a \in \mathbb{Z}^+$, and
$$
\left\{
\begin{array}{rl}
x^3 + \sin x - 2a &= 0 \\
4y^3 +\frac{1}{2}\sin 2y +a &=0
\end{array}
\right.
$$
Compute the value of $\cos(x+2y)$
Find the range of the function $$y=x+\sqrt{x^2 -3x+2}$$
Which pair contains same functions:
(A) $f(x)=\sqrt{(x-1)^2}$ and $g(x)=x-1$
(B) $f(x)=\sqrt{x^2 -1}$ and $g(x)=\sqrt{x+1}\cdot\sqrt{x-1}$
(C) $f(x)=(\sqrt{x -1})^2$ and $g(x)=\sqrt{(x-1)^2}$
(D) $f(x)\displaystyle\sqrt{\frac{x^2-1}{x+1}}$ and $g(x)=\displaystyle\frac{\sqrt{x^2-1}}{\sqrt{x+1}}$
Select all correct answers.
Let $a$ and $k$ be two positive integers, and function $f(x)=3x+1$. If $f(x)$'s domain is $\{1, 2, 3, k\}$ and range is $\{4, 7, a^4, a^2 + 3a\}$, find the value of $a$ and $k$.
Which of the following function is the same as $y=\sqrt{-2x^3}$?
(A) $y=x\sqrt{-2x}\qquad$ (B) $y=-x\sqrt{-2x}\qquad$ (C) $y=-\sqrt{2x^3}\qquad$ (D) $y=x^2\sqrt{-2/x}$
Let $f(x)$ be an odd function and $g(x)$ be an even function. If $f(x)+g(x)=\frac{1}{x-1}$, find $f(x)$ and $g(x)$.
If $f\Big(\displaystyle\frac{x+1}{x}\Big)=\displaystyle\frac{x^2+x+1}{x^2}$, find $f(x)$.
If $f(x)$ is an odd function defined on $\mathbb{R}$, compute $f(0)$.
Let $f(x)= \sqrt{ax^2+bx}$. For how many real values of $a$ is there at least one positive value of $b$ for which the domain of $f$ and the range of $f$ are the same set?
The nonzero coefficients of a polynomial $P$ with real coefficients are all replaced by their mean to form a polynomial $Q$. Which of the following could be a graph of $y = P(x)$ and $y = Q(x)$ over the interval $-4\leq x \leq 4$?
![](data:image/png;base64,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)
The graph of the function $f$ is shown below. How many solutions does the equation $f(f(x))=6$ have?
Determine all polynomials such that $P(0) = 0$ and $P(x^2 + 1) = P(x)^2 + 1$.
A binary operation $\diamondsuit$ has the properties that $a\,\diamondsuit\, (b\,\diamondsuit \,c) = (a\,\diamondsuit \,b)\cdot c$ and that $a\,\diamondsuit \,a=1$ for all nonzero real numbers $a, b,$ and $c$. (Here $\cdot$ represents multiplication). The solution to the equation $2016 \,\diamondsuit\, (6\,\diamondsuit\, x)=100$ can be written as $\tfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. What is $p+q?$
Let $f(x)=x^{-\frac{k^2}{2}+\frac{3}{2}k+1}$ be an odd function where $k$ is an integer. If $f(x)$ is monotonically increasing when $x\in(0,+\infty)$, find all the possible values of $k$.
Let $P(x)$ be a nonzero polynomial such that $(x-1)P(x+1)=(x+2)P(x)$ for every real $x$, and $(P(2))^2 = P(3)$. Then $P\big(\frac72\big)=\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$x^2f(x)+f(1-x)=2x-x^4$$
Find all functions $f:\mathbb{Q}\rightarrow\mathbb{Q}$ such that the Cauchy equation $$f(x+y)=f(x)+f(y)$$ holds for all $x, q\in\mathbb{Q}$.
Find the range of function $y=x+\sqrt{x^2 -3x+2}$.
Solve $$\Big|\frac{1}{\log_{\frac{1}{2}}x+2}\Big|> \frac{3}{2}$$