Question

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

Answer 1

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

I'm assuming you mean the function $f(x)=x^{\frac{1}{5}}$.  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!