We are given the following function:
![f(x)=(x-3)/(2)](https://img.qammunity.org/2023/formulas/mathematics/college/xrtx935vkun7fdsnjf18wzv5irl72h3c75.png)
We are asked to determine:
![f^(-1)(x)](https://img.qammunity.org/2023/formulas/mathematics/college/waf784241cxsbeinwxex430qxcslo7ew4e.png)
This is called the inverse function.
To do that we will first switch the value of the variables f(x) and "x" as follows:
![x=(f(x)-3)/(2)](https://img.qammunity.org/2023/formulas/mathematics/college/ihcwl6x7tl0ctgt584icfl0uuxae1zqo11.png)
Now, we will solve for f(x). To do that we will multiply both sides by 2:
![2x=f(x)-3](https://img.qammunity.org/2023/formulas/mathematics/college/3vcjivmwx4b6xj3r5sa50oeeu4jrqbr9s8.png)
Now we add 3:
![2x+3=f(x)](https://img.qammunity.org/2023/formulas/mathematics/college/5pzp5hdp7yidg0p1883j2srz4tmf8vxl4j.png)
This is the inverse, therefore, we change:
![f(x)=f^(-1)(x)](https://img.qammunity.org/2023/formulas/mathematics/college/8pdzik9jsudy9387hq47am9660eicxlgfy.png)
Therefore, we have:
![f^(-1)(x)=2x+3](https://img.qammunity.org/2023/formulas/mathematics/college/hfct7olpe739k3gky3la0vtiyngddjwho9.png)