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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


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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