The functions which map [-1, 1] to [0, 2] are | vedclass

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(B) linear function is of the form $f(x) = ax + b$. We want to map the interval $[-1, 1]$ to $[0, 2]$. Case $1$: $f(-1) = 0$ and $f(1) = 2$. $-a + b =

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Two linear functions

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(B) linear function is of the form $f(x) = ax + b$. We want to map the interval $[-1, 1]$ to $[0, 2]$. Case $1$: $f(-1) = 0$ and $f(1) = 2$. $-a + b = 0 \implies a = b$. $a + b = 2 \implies 2a = 2 \implies a = 1, b = 1$. So,$f(x) = x + 1$. Case $2$: $f(-1) = 2$ and $f(1) = 0$. $-a + b = 2$. $a + b = 0 \implies b = -a$. $-a - a = 2 \implies -2a = 2 \implies a = -1, b = 1$. So,$f(x) = -x + 1$. Thus,there are two such linear functions.

The functions which map $[-1, 1]$ to $[0, 2]$ are

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