I think you're getting lost in the symbolism. The question is asking whetherterp.asessed said:Homework Statement
Determine whether or not the following pairs of operators commute...and there was one I could not solve...according to the back of the textbook, I do understand 14.c does NOT commute, but I don't understand...
(14)c.
A = SQR
B = SQRT
Homework Equations
ABf(x) - BAf(x) = 0
The Attempt at a Solution
ABf(x) = A[f(x)]1/2 = f(x)
BAf(x) = Bf2(x) = f(x)...so I thought they DO commute, but the textbook says NO! Could someone explain? Thanks!
Mark44 said:##(\sqrt{f(x)})^2 = \sqrt{(f(x))^2}##
Can you always take the square root of something?
Right. That's why the two operations don't commute. Good!terp.asessed said:Come to think of it, one can't square root of the function that is negative...so NOT always...
Operators A and B refer to two mathematical operations that can be performed on a set of numbers or variables. These operations can include addition, subtraction, multiplication, and division.
For Operators A and B to commute means that the order in which these operations are performed does not affect the end result. In other words, if we apply Operator A first and then Operator B, or vice versa, we will get the same result.
The commutative property is important because it allows us to manipulate mathematical expressions more easily. It also helps us to simplify complex equations and solve problems more efficiently.
Yes, there are cases where Operators A and B do not commute. This can occur when one of the operations is not commutative, such as division or subtraction. In these cases, the order of operations does matter and can affect the end result.
To determine if Operators A and B commute, we can perform a simple test by applying the operations to a set of numbers in different orders and comparing the results. If the results are the same, then the operators commute. If the results are different, then the operators do not commute.