Answer:
To find the inverse of the function.
Given function is,
![g(x)=-(3)/(5)x](https://img.qammunity.org/2023/formulas/mathematics/college/dzx3mkm198j596clqviqfot5dd84cz0gbf.png)
we know that,
The inverse function returns the original value for which a function gave the output.
Consider the function,
![y=-(3)/(5)x](https://img.qammunity.org/2023/formulas/mathematics/college/2dhdf3dvu20o6vyftug4i7amczf4zp5kzy.png)
replace x by y and y by x, we get,
![x=-(3)/(5)y](https://img.qammunity.org/2023/formulas/mathematics/college/wqbxvazxw2f38klwaod9a7tfro17dupedy.png)
Solve for y we get,
![-3y=5x](https://img.qammunity.org/2023/formulas/mathematics/college/gv1wi3ds0kssgjdxjj32ca0vdkvdm8ffxf.png)
![y=-(5)/(3)x](https://img.qammunity.org/2023/formulas/mathematics/college/pevtuq32p845gekefqb2c6yk45398no5rg.png)
The inverse function f(x) is,
![f(x)=-(5)/(3)x](https://img.qammunity.org/2023/formulas/mathematics/college/32pm4ofzrt3hy8da6rjzczjajo4f0kwyie.png)
The inverse function is,
![f(x)=-(5)/(3)x](https://img.qammunity.org/2023/formulas/mathematics/college/32pm4ofzrt3hy8da6rjzczjajo4f0kwyie.png)