+99 20. (a) For all real numbers a and b, |a + b| = |a| + |b|
(b) For all real numbers a and b, bac + bbc = ba + bc.
(c) If f(x) and g(x) are linear functions, then f (g(x)) is a linear function.
+983 If you want me to prove these statements, here is the proof:
(a) is not true, all we need to do is show an example that doesn't satisfy these claims to counter the statement.
We say a = -2 and b = 3
\(|(-2)+3|=1\), \(|-2|+|3|=5\)
\(1\ne5\), therefore (a) is not true.
(b)
We once again can plug in numbers.
a = 0 and b = 2
0 + 4c = 0 + 2c
4 is not equal to 2, so (b) is not true.
(c)
This is true
