Prove that if f: X -> R is continuous and [a,b] is a subset of X, then f([a,b]) = (c,d) for some c,d in R. (R = real numbers)

Prove that if f: X -> R is continuous and [a,b] is a subset of X, then f([a,b]) = (c,d)
for some c,d in R. (R = real numbers)
 
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