Question

Find the inverse of the function below. When typing your answer use the "^" key (shift+6) to indicate an exponent. For example, if we have x squared (x times x) we would type x^2. f(x)= \frac{x+3}{x+7} The numerator of f^{-1}(x) is Answer - AnswerThe denominator of f^{-1}(x) is Answer - Answer

Answer 1

To determine the inverse function, we will write the function and reach the inversion by performing the required calculation, as follows:

$\begin{gathered} y=\frac{x+3}{x+7}\Rightarrow y(x+7)=x+3 \\ y\cdot x+7y=x+3\Rightarrow x\cdot y-x=3-7y \\ x(y-1)=3-7y \\ \\ x=\frac{3-7y}{y-1} \end{gathered}$

From the solution developed above, we are able to conclude that the solution for the present question is the following:

$f^{-1}(x)=\frac{3-7x}{x-1}$

Where the numerator is: 3 - 7x

Ans the denominator is: x - 1