令a=x²+2x+2=(x+1)²+1
x∈[-3,2],∴x+1∈[-2,3] => 0≤(x+1)²≤9
=> 1≤a≤10 => 1/10≤1/a≤1
而y=(a-2)/a=1-2/a,由上知-2≤-2/a≤-1/5
∴-1≤y≤4/5