Functions

Concept Quizzes

Evaluating Functions
Function Arithmetic
Function Terminology
Composition of Functions
Inverse Functions
Function Misconceptions
Symbolic Operators
Function Problem Solving

Challenge Quizzes

Functions: Level 1 Challenges
Functions: Level 2 Challenges
Functions: Level 3 Challenges
Functions: Level 4 Challenges
Functions: Level 5 Challenges

Symbolic Operators

For positive integer $k$ , let $\bullet k\bullet = k^{2}-(k-1)^{2}$ . What is the value of $\bullet 7\bullet$ ?

(A) $\ \ -36$
(B) $\ \ 7$
(C) $\ \ 13$
(D) $\ \ 49$
(E) $\ \ 85$

A B C D E

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by Brilliant Staff

For positive integers $m$ and $n$ , let $m \nabla n$ be defined as $m \nabla n = (\frac{m}{n})^{-1} - (\frac{n}{m})^{-1}$ . What is the value of $2 \nabla 15$ ?

(A) $\ \ -\frac{15}{2}$

(B) $\ \ -\frac{221}{30}$

(D) $\ \ \frac{2}{15}$

(E) $\ \ \frac{229}{30}$

A B C D E

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by Brilliant Staff

For positive integers $m$ , $k$ , and $n$ , let $m\breve{k}n$ be defined as $m\breve{k}n = k\frac{m}{n}$ , where $k\frac{m}{n}$ is a mixed fraction. What is the value of $6\breve{4}1 + 1\breve{4}6$ ?

(A) $\ \ 0$

(B) $\ \ 5$

(D) $\ \ 700$

(E) $\ \ 787$

A B C D E

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For positive integers, $x$ , $y$ , and $z$ , let $\widehat{x,y,z}$ be defined by $\widehat{x,y,z} = zx - yz - xy$ . What is the value of $m$ if $\widehat{10,m,10} = \widehat{7,3,1}?$

(A) $\ \ -\frac{631}{20}$

(B) $\ \ -\frac{117}{20}$

(D) $\ \ \frac{21}{100}$

(E) $\ \ \frac{117}{20}$

A B C D E

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For a positive integer $n$ , let $\fbox{n} = 1-2+3-4 \ldots n$ . For example, $\fbox{5}=1-2+3-4+5=3.$ Which of the following is equal to $\fbox{6}-\fbox{48}$ ?

(A) $\ \ -1155$
(B) $\ \ -27$
(C) $\ \ -21$
(D) $\ \ -\fbox{6}$
(E) $\ \ 21$

A B C D E

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by Brilliant Staff