When is a function neither odd or even?For example why is x^3/2 neither odd or even?
When the domain is R\{0}, is the range always R+?
How do u find {x:x^3/2>x^2 } and {x:x^-3/2<x^-2}?
$\displaystyle \frac {x^3}2$ is odd. did you mean to say $\displaystyle x^{3/2}$ ?
a function f(x) is even if f(-x) = f(x)
a function is odd if f(-x) = -f(x)
otherwise, it is neither
consider the function f(x) = 1/xWhen the domain is R\{0}, is the range always R+?
set up your inequalities and solve for xHow do u find {x:x^3/2>x^2 } and {x:x^-3/2<x^-2}?
can you solve $\displaystyle x^{3/2} > x^2$ for x? (is the power 3/2? type clearly)
we have $\displaystyle 1 > \sqrt{x}$
note that the domain of the square root function is $\displaystyle x \ge 0$, so we must have that for $\displaystyle \sqrt{x}$ to make sense. however, we drop the $\displaystyle x = 0$ part, because that does not work in the original inequality.
now, if we square both sides, we get: $\displaystyle 1 > x$
so we have $\displaystyle 0< x$ and $\displaystyle x < 1$, hence $\displaystyle 0 < x < 1$