Answer
one-to-one function
inverse: $f^{-1}(x)=\dfrac{x-7}{-3}$
Work Step by Step
Some of the ordered pairs of the given function, $
f(x)=-3x+7
$, are $
\left\{(-2,13)(-1,10),(0,7),(1,4),(2,1),...\right\}
$. Note that every $y$-coordinate from this function is unique. Hence, the given function is a one-to-one function.
To find the inverse, let $y=f(x)$. Then, interchange the $x$ and $y$ variables and solve for $y$. That is,
\begin{align*}\require{cancel}
y&=-3x+7
\\&\Rightarrow
x=-3y+7
&(\text{interchange $x$ and $y$})
\\&
x-7=-3y
&(\text{solve for $y$})
\\\\&
\dfrac{x-7}{-3}=\dfrac{\cancel{-3}y}{\cancel{-3}}
\\\\&
\dfrac{x-7}{-3}=y
.\end{align*}
Hence, the inverse is $
f^{-1}(x)=\dfrac{x-7}{-3}
$.
