The one$-$to$-$one function $f$ is defined below.

$f(x)=\frac{4x-7}{7x+1}$

Find $f^{-1}(x),$ where $f^{-1}$ is the inverse of $f.$

Also state the domain and range of $f^{-1}$ in interval notation.

$f^{-1}(x)=\frac{x+7}{4-7x}$

Domain of $f^{-1}=$

Range of $f^{-1}=$