Answer
Evaluate $ f (x) = \frac{1-2x}{3} $:
$$ f (2) = -1 $$
$$ f (-2) = \frac{5}{3} = 1.6667 $$
$$ f (\frac{1}{2}) = 0$$
$$ f (a) = \frac{1-2(a)}{3}$$
$$ f (-a) = \frac{1+2a}{3} $$
$$ f (a-1) = \frac{-2}{3}a + 1 $$
Work Step by Step
x = 2
$$ f (2) = \frac{1-2(2)}{3} $$
multiply $2\times(2)$
$$ f (2) = \frac{1-4}{3} $$
subtract $1-4$
$$ f (2) =\frac{-3}{3} $$
divide $\frac{-3}{3}$
$$ f (2) = -1 $$
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x = -2
$$ f (-2) = \frac{1-2(-2)}{3} $$
multiply $2\times(-2)$
$$ f (-2) = \frac{1-(-4)}{3} $$
subtract $1-(-4)$
$$ f (-2) =\frac{5}{3} $$
divide $\frac{5}{3}$
$$ f (-2) = 1.6667 $$
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x = $\frac{1}{2}$
$$ f (\frac{1}{2}) = \frac{1-2(\frac{1}{2})}{3} $$
multiply $2\times(\frac{1}{2})$
$$ f (\frac{1}{2}) = \frac{1-1}{3} $$
subtract $1-(1)$
$$ f (\frac{1}{2}) =\frac{0}{3} $$
divide $\frac{0}{3}$
$$ f (\frac{1}{2}) = 0 $$
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x = a
$$ f (a) = \frac{1-2(a)}{3} $$
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x = -a
$$ f (-a) = \frac{1-2(-a)}{3} $$
multiply $2\times(-a)$
$$ f (-a) = \frac{1-(-2a)}{3} $$
$$= \frac{1+2a}{3} $$
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x = a - 1
$$ f (a-1) = \frac{1-2(a-1)}{3} $$
multiply $2\times(a-1)$
$$ f (a-1) = \frac{1-(2a-2)}{3} $$
subtract $1-(2a-2)$ or add $1+ (-2a + 2)$
$$ f (a-1) =\frac{-2a+3}{3} $$
divide and simplify $\frac{-2a+3}{3}$
$$ f (a-1) = \frac{-2}{3}a + \frac{3}{3}$$
$$ = \frac{-2}{3}a + 1$$
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