We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
224
1
avatar+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.

 May 19, 2018
 #1
avatar+988 
+1

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

 

winkwinkwink

 May 19, 2018
edited by GYanggg  May 19, 2018

7 Online Users