Let A -1-2-3- - 10 and f - A - A be defined as f k - left begin matrix k -1 - itext if k is odd k - text if k is even lend matrix right- Then the number of possible functions g - A - A such that gof - f is- 105B- 10 C 5- 55D- 5 -

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Determinant

Let A =1,2,3,...

Question

Let $A = {1, 2, 3, . . . ., 10}$ and $f : A \to A$ be defined as $f (k) = {\begin{matrix} k + 1 & if k is odd k & if k is even \end{matrix} .$ Then the number of possible functions $g : A \to A$ such that $g o f = f$ is:

10^{5}

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^{10} C_{5}

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5^{5}

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5!

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Solution

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Similar questions

A = {1, 2, 3, . . . ., 10}

f : A \to A

f (k) = {\begin{matrix} k + 1 & if k is odd k & if k is even \end{matrix} .

g : A \to A

g o f = f

f

f (n) = {\begin{matrix} n + 3 & if n is odd \frac{n}{2} & if n is even \end{matrix}

k

f (f (f (k))) = 27

k

f

(- \frac{1}{3}, \frac{1}{3})

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{1}{x} {log}_{e} (\frac{1 + 3 x}{1 - 2 x}), when x \neq 0 k, when x = 0 \end{matrix}

k

(\begin{matrix} n k \end{matrix})

^{n} C_{k}

[\begin{matrix} n k \end{matrix}] = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} (\begin{matrix} n k \end{matrix}), & if 0 \leq k \leq n 0, & otherwise. \end{matrix}

A_{k} = 9 \sum i = 0 (\begin{matrix} 9 i \end{matrix}) [\begin{matrix} 12 12 - k + i \end{matrix}] + 8 \sum i = 0 (\begin{matrix} 8 i \end{matrix}) [\begin{matrix} 13 13 - k + i \end{matrix}]

A_{4} - A_{3} = 190 p,

p

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{(sin x) (e^{x} - 1)}{x log (1 + x)}, k, \end{matrix} \begin{matrix} x \neq 0 x = 0 \end{matrix}

f (x)

x = 0

k

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