The problem came up when I was asked to compose two functions and determine if the composed function is one to one, onto, or neither.
Full link to the question :
I defined h(x) = x^4, g(x) = surd(x,8).
I wanted to show that the composition f=h(g(x)) is not onto by showing there is no solution
to h(g(x) = -2.
The root command might be better for solving equations than the surd.
Here is a screenshot, with both surd and rational exponents for comparison.
The root(x) command gives me the expected response of no solution.
Should I just stick with rational exponents?
It would be nice if Maple would say 'no solution' when there is no result.
Otherwise someone might think their version of Maple is buggy or something.
Also I notice Maple does not simplify exponents by default. For example (x^4)^(1/8) does not become x^(1/2).
One way seems to be to make an assumption.