For this case we have to find the inverse of a function, follow the steps below:
- We exchange the variables.
- Finally we change y by
![f ^ {- 1} (x)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/aqxu0nzet5gtci09zxse9j36cnge374km7.png)
Then, it is observed that of option 3:
![f (x) = 4x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qedfz837ksug78nnvc30q6r5nyeyhdi4uz.png)
Replace
with y:
![y = 4x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/96eu19dmcrdu96ybk3j1mzm1ckuda2x5vu.png)
We exchange the variables:
![x = 4y](https://img.qammunity.org/2020/formulas/mathematics/middle-school/acagpmf4s9rs8bh3zegxfyggaioqi1tfhn.png)
We solve for "y":
![4y = x\\y = \frac {x} {4}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jrgqz4w91q4kr592uepka9naw4tyk5t8ap.png)
Finally we change y by
![f ^ {- 1} (x):](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ggc3z2p7x17msi7c3efapzety0ez3x7d5b.png)
![f ^ {- 1} (x) = \frac {x} {4}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/s5wkdengn4my6daqtg5l3t4p45ykqv4dou.png)
Answer:
The correct option is C