Answer
one-to-one function
inverse: $f^{-1}(x)=\dfrac{x-1}{3}$
Work Step by Step
Some of the ordered pairs of the given function, $
f(x)=3x+1
$, are $
\left\{(-2,-5)(-1,-2),(0,1),(1,4),(2,7),...\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+1
\\&\Rightarrow
x=3y+1
&(\text{interchange $x$ and $y$})
\\&
x-1=3y
&(\text{solve for $y$})
\\\\&
\dfrac{x-1}{3}=\dfrac{\cancel3y}{\cancel3}
\\\\&
\dfrac{x-1}{3}=y
\\\\&
y=\dfrac{x-1}{3}
.\end{align*}
Hence, the inverse is $
f^{-1}(x)=\dfrac{x-1}{3}
$.
