Question

Let f(x) = $|x-3|$ +$|x-5|$

Then f(x) = 2x - 8 if x $\ge$ 5

= 8 - 2x if x $\le$ 3

• A. True
• B. False

Answer 1

The correct option is A

True

$|x-3|$ = x-3 if x > 3

= 3 - x if x < 3

$|x-5|$ = x-5 if x>5

= 5 - x if x< 5

So, we have to split the function f at the point 3 and 5. There will be three elements.

So for x<3 f(x) = 3-x + 5-x = 8-2x
For x>5 f(x) = x-3+x-5 = 2x-8