Theorem 323 Suppose that the functions fDR is monotone If it

Solution

3. a)

Given D = [0,1] U [2,3]

From the definition of f(x),

f(0) = 0

f(1) = 1

f(2) = 2²-3=1

f(3) = 3²-3=6

so, f(D) = [0,1] U [1,6] for D = [0,1]U[2,3], which is an interval, hence f is continuous.

3. b)

Since, f(1) = 1 = f(2), thus the function f is continuous for every value of D.