Question

Which function is not a power function?
f(x) = x
f(x) = x^1/3
f(x) = 1/x
f(x) = |x|

Answer 1

any ideas?

Answer 2

hint: \(\bf x^{\frac{1}{3}}\impliedby obvious
\\ \quad \\
\cfrac{1}{x}\iff x^{-1}\impliedby \textit{also a power one}
\\ \quad \\
|x|\iff +x,-x\iff \sqrt{x^2}\implies (x^2)^{\frac{1}{2}}\)

Answer 3

so |x|?

Answer 4

hmmm well... nope obvously is a power function, since it uses power to get the +/- signs

\(\bf x \iff x^1\) to be fair, however, a 1 itself, doesn't make it a power function
so, it'd be "x"

Answer 5

https://en.wikipedia.org/wiki/Power_function

Answer 6

you are correct... \(|x|\) is not a power function