m=√(8-x²)+x+1∵8-x²≥0∴令x=2√2cosα0≤α≤π
∴m=2√2sinα+2√2cosα +1=2√2(sinα +cosα )+1=4sin(α+π/4)+1
∵0≤α≤π∴π/4≤α+π/4≤5π/4
∴-√2/2≤sin(α+π/4)≤1
1-2√2≤4sin(α+π/4)+1≤5
1-2√2≤m≤5