OK....this seems a little confusing....but it's not too bad....
First, we need to see that x= √2 ≤ pi.....so this tells us that we should use the first piecewise function to evaluate h(√2)..so we have
h(√2) = floor (4√2) = 5
Now.....we want to put this result back into h(x)...but note....now we must use the piecewise function 3 - x since the "x" we're putting into h lies between pi and 5.2
So we have
f(5) = 3 - 5 = -2
So h(h(√2)) just evaluates to -2
OK....this seems a little confusing....but it's not too bad....
First, we need to see that x= √2 ≤ pi.....so this tells us that we should use the first piecewise function to evaluate h(√2)..so we have
h(√2) = floor (4√2) = 5
Now.....we want to put this result back into h(x)...but note....now we must use the piecewise function 3 - x since the "x" we're putting into h lies between pi and 5.2
So we have
f(5) = 3 - 5 = -2
So h(h(√2)) just evaluates to -2