# Domain of One Variable Function – A function to the power of a constant – Exercise 2471

Exercise

Determine the domain of the function:

$$f(x)={(-x)}^{\frac{5}{2}}$$

$$x\leq 0$$

Solution

Let’s find the domain of the function:

$$f(x)={(-x)}^{\frac{5}{2}}$$

We rearrange it:

$$f(x)={(-x)}^{\frac{5}{2}}=\sqrt{{(-x)}^5}$$

Since we have a square root, we require the expression inside the root to be non-negative:

$${(-x)}^5\geq 0$$

And this holds when

$$-x\geq 0$$

$$x\leq 0$$

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