Questions: f(x)=4/(x+7)

Solution Steps

To find the inverse of the function $f(x) = \frac{4}{x+7}$, we need to swap the roles of $x$ and $y$ and solve for $y$. This involves setting $y = \frac{4}{x+7}$, then solving for $x$ in terms of $y$, and finally expressing $y$ as a function of $x$.

To find the inverse of the function $f(x) = \frac{4}{x+7}$, we start by setting $y = \frac{4}{x+7}$.

Next, we swap $x$ and $y$ to get $x = \frac{4}{y+7}$. We then solve for $y$ in terms of $x$.

Rearranging the equation $x = \frac{4}{y+7}$, we multiply both sides by $y+7$ to get: $$x(y+7) = 4$$

Expanding and solving for $y$, we have: $$xy + 7x = 4$$ $$xy = 4 - 7x$$ $$y = \frac{4 - 7x}{x}$$

Final Answer