A piecewise function p is defined by
p(x)=⎩⎨⎧x+2,4−x,x−42,x<−1,−1≤x≤4,x>4.
Another function is q(t)=5t−t2. Answer the following questions about the composite function q∘p.
a. (i) For the branch x<−1, find all x such that q(p(x)) is real.
b. (ii) Repeat part (i) for the branch −1≤x≤4.
c. (iii) Repeat part (i) for the branch x>4.
d. (iv) Combine your results to write the complete domain of q∘p and show that it can be expressed as the union of two disjoint intervals.