# Domain of Combinations of Functions

### Instructions

- This page includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.

### Concepts

- Finding the domain of functions with combinations of denominators, even roots, and/or logarithms

### Exercises

**Directions:**You should attempt to solve the problems first and then watch the video to see the solution.

- Find the domain of the following function \(f(x)=\frac{x}{x-5}+\sqrt{x-1}+\log_5(x+6).\)

- Find the domain of the function \(f(x)=\dfrac{\ln(x)}{x^2-x-6}.\)

- Find the domain of the function \(f(x)=\dfrac{x^3-9x}{\sqrt{3x+3}}.\)

- Find the domain of the function \(f(x)=\dfrac{\sqrt[4]{x+4}}{\log_7(5-3x)}\)