Precalculus: Mathematics for Calculus, 7th Edition

Evaluate $f (x) = \frac{1-2x}{3}$: $$f (2) = -1$$ $$f (-2) = \frac{5}{3} = 1.6667$$ $$f (\frac{1}{2}) = 0$$ $$f (a) = \frac{1-2(a)}{3}$$ $$f (-a) = \frac{1+2a}{3}$$ $$f (a-1) = \frac{-2}{3}a + 1$$
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 $\frac{-3}{3}$ $$f (2) = -1$$ -------------------------- 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 $\frac{5}{3}$ $$f (-2) = 1.6667$$ -------------------------- 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 $\frac{0}{3}$ $$f (\frac{1}{2}) = 0$$ -------------------------- x = a $$f (a) = \frac{1-2(a)}{3}$$ -------------------------- x = -a $$f (-a) = \frac{1-2(-a)}{3}$$ multiply $2\times(-a)$ $$f (-a) = \frac{1-(-2a)}{3}$$ $$= \frac{1+2a}{3}$$ -------------------------- 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 $\frac{-2a+3}{3}$ $$f (a-1) = \frac{-2}{3}a + \frac{3}{3}$$ $$= \frac{-2}{3}a + 1$$ --------------------------