Question 16 of 20
Determine whether the function is one-to-one. If it is, find a formula for its inverse.
$$f(x)=\frac{7}{x+3}$$

Is the function one-to-one?
No
Yes

What is the inverse function? Select the correct choice below and fill in the answer box within your choice if necessary.
A. $f^{-1}(x)=◻$
B. The function is not one-to-one.

Step 1 ：First, let's check if the function is one-to-one. We can do this by checking if the derivative of the function is always positive or always negative. If it is, then the function is one-to-one.

Step 2 ：Let's find the derivative of the function $f(x)=\frac{7}{x+3}$. The derivative $f^{\prime }(x)$ is $-\frac{7}{{(x+3)}^2}$.

Step 3 ：Since the derivative of the function is always negative, the function is one-to-one.

Step 4 ：Next, let's find the inverse of the function. We can do this by swapping x and y in the equation and solving for y.

Step 5 ：The inverse of the function is $f^{-1}(x)=-3+\frac{7}{x}$.

Step 6 ：$\boxed{{\displaystyle \text{The function is one-to-one and its inverse is }{f}^{-1}(x)=-3+\frac{7}{x}}}$