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Find a formula for the inverse, that is find \(\displaystyle f^{-1}(x)\) if \(\displaystyle f(x)=\frac{- 4 x - 5}{4 x + 7}\).

\(\displaystyle f^{-1}(x)=- \frac{7 x + 5}{4 x + 4}\)

Download \(\LaTeX\)

\begin{question}Find a formula for the inverse, that is find $f^{-1}(x)$ if $f(x)=\frac{- 4 x - 5}{4 x + 7}$.
    \soln{9cm}{$f^{-1}(x)=- \frac{7 x + 5}{4 x + 4}$}

\end{question}

Download Question and Solution Environment\(\LaTeX\)

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

Find a formula for the inverse, that is find <img class="equation_image" title=" \displaystyle f^{-1}(x) " src="/equation_images/%20%5Cdisplaystyle%20f%5E%7B-1%7D%28x%29%20" alt="LaTeX: \displaystyle f^{-1}(x) " data-equation-content=" \displaystyle f^{-1}(x) " /> if <img class="equation_image" title=" \displaystyle f(x)=\frac{- 4 x - 5}{4 x + 7} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D%5Cfrac%7B-%204%20x%20-%205%7D%7B4%20x%20%2B%207%7D%20" alt="LaTeX: \displaystyle f(x)=\frac{- 4 x - 5}{4 x + 7} " data-equation-content=" \displaystyle f(x)=\frac{- 4 x - 5}{4 x + 7} " /> .