Let f and g be real-valued functions defined on an interval I and suppose that both are continuous at x=c∈I.
a. (i) State the definition of continuity of a function at a point.
b. (ii) Using only the definition in part (i), explain why f+g is continuous at x=c.
c. (iii) Give one pair of real functions that are continuous everywhere on R and show, in one or two sentences, why their difference is continuous at every real number.