Problem

(a) Find the inverse function of $f(x)=7 x-6$. \[ f^{-1}(x)= \] (b) The graphs of $f$ and $f^{-1}$ are symmetric with respect to the line defined by $y=$

Solution

Step 1 :The inverse function of a function can be found by swapping the x and y values and solving for y. In this case, we need to find the inverse of \(f(x)=7x-6\). This means we need to solve the equation \(x=7y-6\) for y.

Step 2 :Solving the equation \(x=7y-6\) for y, we get \(y=\frac{x}{7}+\frac{6}{7}\).

Step 3 :So, the inverse function of \(f(x)=7x-6\) is \(f^{-1}(x)=\frac{x}{7}+\frac{6}{7}\).

Step 4 :Final Answer: The inverse function of \(f(x)=7x-6\) is \(f^{-1}(x)=\boxed{\frac{x}{7}+\frac{6}{7}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/23677/

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