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If two functions like f(x) and g(x) having range within an finite interval

If two functions like f(x) and g(x) having range within an finite interval , and let there be another function h(x) which is h(x)=f(x)+g(x), then do the range of h(x) will be just adding the inequality of the two individual functions range?

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Let f:D1----> R and g:D2---->R be two real functions, then their sum f+g defined as that function from D1 intersection D2 to R which associates each x belongs to D1 intersection D2 to the number f(x) + g(x), hence h(x)will be just adding the inequality of the two individual functions range

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