Suppose that f(x) and g(x) are functions on R such that the range of f is [-5,3], and the range of g is [-2,1]. The range of f(x) + g(x) is [a,b]. What is the largest possible value of b?
+9675 The maximum of f(x) + g(x) is always not greater than the maximum of f(x) + the maximum of g(x) because if the maximum point of f(x) and the maximum of g(x) point is not aligned on a vertical line, the maximum of f(x) + g(x) is going to be smaller.
That means, max(f(x)+g(x))=b≤max(f(x))+max(g(x))=3+1=4.
Then b≤4.
