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

Exercise

Determine the domain of the function:

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

Final Answer

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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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