Question

What are the domain range of f(x)= 1/5 power of x

Answer 1

Domain: all real numbers

Range: all real numbers

Explanation:

I'm assuming you mean the function
`f(x)=x^{(1)/(5)}`. That's usually written

f(x) = x^(1/5) with the ^ meaning "to the power of..." and the fraction exponent in parentheses so as not to be confused with x^1/5 which could mean x to the first power, divided by 5.

Fractional exponents are used to indicate roots. In this case, x is being raised to the 1/5 power, so this is the fifth root of x, written
`\sqrt[5]{x}`. The 5 is called the root index.

For odd roots, like this one, the domain is all real numbers--x can be any number at all. So the domain is all real numbers.

The range is also all real numbers. Attached is a graph of this function. It might not look like it, but the graph rises to the right to any height. The larger x gets, the larger the 5th root gets. A similar thing happens on the left--the smaller x gets, the smaller the 5th root gets.

EDIT: see the comment. For the function
`f(x)=(1/5)^x`, the domain is all real numbers. The range is positive real numbers. I'll attach a graph!