Question

Let $f\left(x\right)=|x-5|–1,g\left(x\right)=4–|x|$ , then the set of all points where fog is discontinuous , is

• A. An empty set
• B. {0}
• C. {0. 5}
• D. {0, 4, 5}

Answer 1

The correct option is A An empty set

Given $f\left(x\right)=|x-5|–1,g\left(x\right)=4–|x|$
$\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right)=f(4-|x|)$ $=|4-|x|-5|–1$
$=|-|x|-1|–1$
$=||x|+1|–1$
$=|x|+1–1=|x|$
$\therefore$ fog(x) is always continuous function for all x
Set of points of discontinuous = empty set