Mathematics: Find n (a) for the set a = {0,1,2,3,4}

Find n (a) for the set a = {0,1,2,3,4} - id012344621203, datgamer13

Ответ:

coleian24

31.12.2020

Mathematics

answer: 10/3, 5

explanation

essentially, we solve $f(x) = x$ four times on each of the pieces' intervals.

for each piece, we find a value of x such that the piece will be equal to x. then, we see if that particular value of x is in the defined interval of the piece. if it is in the interval, then it is a valid answer. if it is not in the interval, then it is not a valid answer.

these are all linear pieces; therefore, each piece can have at most one x-value such that f(x) = x.

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for the first piece, $2x+1,\ 1\le x\le2$ , we solve

$\begin{aligned}2x+1 & = x \\x + 1 & = 0 \\x & = -1\end{aligned}$

since this x value is not the interval $1\le x\le2$ , we disregard this solution.

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for the second piece, $7-x,\ 2< x\le3$ , we solve

$\begin{aligned} 7-x & = x \\ 7 & = 2x \\x & = 7/2 = 3.5\end{aligned}$

since this x value is not in the interval $2< x\le3$ , we disregard this solution.

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for the third piece, $10-2x,\ 3 < x \le 4$ , we solve

$\begin{aligned}10-2x& = x \\10 & = 3x \\x & = 10/3 = 3.\overline{3}\end{aligned}$

since this x value is in the interval $3 < x \le 4$ defined for this given piece, this is a solution to $f(x) = x$ .

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for the fourth piece, $10-x,\ 4 < x \le 5$ , we solve

$\begin{aligned}10-x & = x \\10 & = 2x \\x & = 5\end{aligned}$

since this x-value is in the interval $4 < x \le 5$ , this is a solution to the equation $f(x) = x$

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Find n (a) for the set a = {0,1,2,3,4}

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