#### Answer

$f(x)=-2x+1$

#### Work Step by Step

We write $f(1)=-1$ as $(1,-1)$ and $f(0)=1$ as $(0,1)$.
Slope of the line that passes through $(1,-1)$ and $(0,1)$ is
$m=\frac{1-(-1)}{0-1}=-2$
The line crosses the y-axis at the point $(0,1)$. So, the y-intercept is $b=1$.
The slope-intercept form is
$y=mx+b$
$\implies y=-2x+1$
A linear function is $f(x)=-2x+1$.