Question

If g:R -->R be two functions defined as f(x)=|x|+x and g(x)=|x|-x for all x belongs to R. Then find fog and gof.

Answer 1

This is a easy concept...
I made a small mistake... it's 4x instead of -4x
think x is greater than 0 let's take x as 1
What will be f o g...look 3rd line
|(|X|-x)|+|x|-x

Put x as 1
|(|1|-1)|+|1|-1= 0
And for all positive values (x>0)
f o g will be zero...

Now take a negative value(x<0)
Let's take -1
f o g become
|(|-1|- (-1))|+|-1|- (-1)
=|1+1|+1+1=4
Thata is 4 × 1
so if x<0 f o g become 4x