# Operators commute?

1. Oct 29, 2014

### terp.asessed

1. The problem statement, all variables and given/known data
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

2. Relevant equations
ABf(x) - BAf(x) = 0

3. 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!

2. Oct 29, 2014

### Staff: Mentor

I think you're getting lost in the symbolism. The question is asking whether
$(\sqrt{f(x)})^2 = \sqrt{(f(x))^2}$
Can you always take the square root of something?

3. Oct 29, 2014

### terp.asessed

Wait, you mean,
are different? I'm sorry, but I'm confused.....

4. Oct 29, 2014

### Staff: Mentor

Well, if they're different, then the two operations aren't commutative. If you believe they are different, why are they different?

I'll ask again, can you always take the square root of something?

5. Oct 29, 2014

### terp.asessed

Come to think of it, one can't square root of the function that is negative.....so NOT always....

6. Oct 29, 2014

### Staff: Mentor

Right. That's why the two operations don't commute. Good!

7. Oct 29, 2014

### terp.asessed

GOTCHA----thank you!

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