Determine whether the statement is true or false.
-Any function of the form $$f ( x ) = x ^ { n }$$ where n is an odd integer, has an inverse.

Question

Quizplus · Accepted Answer

For any odd integer $n$, the function $f(x) = x^n$ is a one-to-one function because it passes both the vertical line test (which determines if it's a function) and the horizontal line test (which determines if it has an inverse). This is because, for odd $n$, the function is strictly increasing or decreasing for all $x$ in its domain, ensuring that each $x$ value maps to a unique $y$ value and vice versa.

Determine Whether the Statement Is True or False f(x)=xnf ( x ) = x ^ { n }f(x)=xn

Determine Whether the Statement Is True or False $f ( x ) = x ^ { n }$