# which of the following is a true statement about functions? Question 11 of 20 3 Points Which of the following is a true statement about functions?

'which of the following is a true statement about functions? Question 11 of 20 3 Points Which of the following is a true statement about functions? A. If fand g are functions, then (f+g) ( = 2) = (g+f( - 2) B. If fis a function then f(2 + h)l =f2) + Ah) 0 C. IfA and Bare matrices then AB can always be computed_ D If fand g are functions then (g cf)lr) = (feg)(x) IPREvIPWN Ai'

### Video Transcript

Which of the following is a true statement about functions so for part a we have f, plus g of negative 2 equals g plus f of negative 2. So this is true why this is true. The reason is that okay, f and g are 2 functions. So, f, f, plus g of x, actually equals f of x, plus g of x. Point okay, so f, plus g of negative 2 equals f of f, 2 f of negative 2 plus g of negative 2, which is of course equals g of f negative 2. Plus, f of negative twont, okay, which equals g plus f of negative 2 point, so i have verified this option a so. This is correct: okay, so for b, if f is the function f of 2 plus h equals f of 2 plus f of h, which is obviously wrong. You just name a random function, like f of x, equals x squared then, okay, if x is 2. There f of 4 equals 16, but f of 2 equals 4, so you cannot have you know f of 4 equals 16 and 16 does not equal to f, f, 4 plus 4. Okay, so therefore, b is wrong for c. If a and b are matrices, then a b can't always be commutated. That is wrong. Okay for c matrix matrix a is, you know, 3 by 2 matrix. If matrix b is 2 by 4, then you can only multiply a to b, but not b to a since. The dimension is different and for d, f, f and g are functions. That g, composed f of x, equals f, composed g of x. Okay, the other is inverse unless f and g are inverse functions. This equation stands otherwise. This equation is invalid, so the only corrct option is a so choose a okay.

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