Fifth Root Function B69336

1. **State the problem:** We are given the function $$f(x) = \sqrt[5]{9 - 11x}$$ and we want to understand or analyze it. 2. **Recall the formula:** The fifth root function is defined as $$f(x) = (9 - 11x)^{\frac{1}{5}}$$. 3. **Domain considerations:** Since the fifth root is an odd root, it is defined for all real numbers, so the domain is all real numbers $$(-\infty, \infty)$$. 4. **Simplify or rewrite:** The function can be written as $$f(x) = (9 - 11x)^{\frac{1}{5}}$$. 5. **Interpretation:** This function takes the expression $$9 - 11x$$ and raises it to the power of $$\frac{1}{5}$$, which means the fifth root. 6. **No restrictions on $$x$$:** Because the fifth root of a negative number is defined, there are no restrictions on $$x$$. 7. **Summary:** The function $$f(x) = \sqrt[5]{9 - 11x}$$ is defined for all real $$x$$ and represents the fifth root of the linear expression $$9 - 11x$$.