Let f(x) be the greatest integer function and g(x) be the modulus function. What is ( g f ) (- 5 3 )-( f g ) (- 5 3 ) equal to?

Step-by-step solution

f(x) greatest integer function f(x)=[x]g(x) modulus function g(x)=|x| aligned & g f(x)=g(f(x)) f o g(x)=f(g(x)) & =g([x]) =f(|x|) & =|[x]| =[|x|] & gof (- 5 3 )= | [- 5 3 ] | ; f o g (- 5 3 )= [ |- 5 3 | ] & =|-2| ; = [ 5 3 ] & =2 ; =1 & gof (- 5 3 )-f o g (- 5 3 )=2-1=1 aligned