Question

If f(x)= l x l and g(x) = [ x ] . Evaluate :
fog ( -5/3 ) - gof ( -5/3 ) .

Answer 1

See the attachment for detail solution
Hope it will help you

Answer 2

∴ The value of $fog(\frac{-5}{3})-gof(\frac{-5}{3} )$ is $0$

Step-by-step explanation:

Given;

$f(x)=\left |x \right |$ and $g(x)=\left [ x \right ]$ then Evaluate $fog(\frac{-5}{3})-gof(\frac{-5}{3} )=?$

So,

$fog(\frac{-5}{3})=f(g(\frac{-5}{3} ))$

∴$g(\frac{-5}{3} )=\left [ \frac{-5}{3} \right ]= \frac{-5}{3}$  (∵$g(x)=\left [ x \right ]=x$ )

Then,

$fog(\frac{-5}{3})=f(\frac{-5}{3} )=\left | \frac{-5}{3} \right |=\frac{5}{3}$ ( ∵$\left | -x\right |=x$ )

Also,

$gof(\frac{-5}{3} )=g(f(\frac{-5}{3} ))$

∴$f(\frac{-5}{3} )=\left | \frac{-5}{3} \right |=\frac{5}{3}$  

Then,

$gof(\frac{-5}{3} )=g(\frac{5}{3} )=\left [ \frac{5}{3} \right ]=\frac{5}{3}$

∴ $fog(\frac{-5}{3})-gof(\frac{-5}{3} )$

$=\frac{5}{3}- \frac{5}{3}$

$=0$

So, the value of $fog(\frac{-5}{3})-gof(\frac{-5}{3} )$ is $0$