Questions: Find the inverse function of the function f(x) = -8/(7x).

Solution Steps

To find the inverse of a function, we need to swap the roles of \(x\) and \(y\) in the equation and then solve for \(y\). Given the function \(f(x) = -\frac{8}{7x}\), we first replace \(f(x)\) with \(y\), then swap \(x\) and \(y\), and finally solve for \(y\) to find the inverse function.

We start with the function given by \( f(x) = -\frac{8}{7x} \). To find the inverse, we will express this in terms of \( y \): \[ y = -\frac{8}{7x} \]

Next, we swap \( x \) and \( y \) to find the inverse function: \[ x = -\frac{8}{7y} \]

Now, we solve for \( y \) in terms of \( x \): \[ 7y \cdot x = -8 \implies y = -\frac{8}{7x} \]

Final Answer