On each of the Venn diagrams below, shade the region which represents the given set. [Figure 1.1 - Three Venn diagrams are shown, with overlapping circles A, B, C within a universal set E. Below each diagram, the set notation is given for which the region is to be shaded.]

The functions f and g are defined, for real values of x greater than 2, by f(x) = 2ˣ - 1, g(x) = x(x + 1).

The function f is defined by f(x) = 2 - √x+5 for -5 ≤ x < 0.

A function f is defined, for all real x, by f(x) = x - x². Find the greatest value of f(x) and the value of x for whi…

Given that A = [[2, -1], [3, 5]], find A⁻¹.

Using your answer from part (i), or otherwise, find the value of a such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] w…

Using your answer from part (i), or otherwise, find the value of b such that A[[a, b], [c, -1]] = [[7, 5], [17, d]] w…