Graph the function f(x) = x³ and \(g(x)=\sqrt[3]x\) on the same co-ordinate plane. Find f o g and graph it on the plane as well. Explain your results.

Write the steps to obtain the graph of the function y = 3(x-1)²+5 from the graph y = x²

By taking suitable sets A, B, C, verify the following results:
(A\(\times\) B)\(\cap \)(B\(\times\)A) = (A\(\cap \)B) \(\times\) (B\(\cap \)A)

By taking suitable sets A, B, C, verify the following results:
C-(B-A) = (C\(\cap \) A) \(\cup \) (C\(\cap \)B')

If A\(\times\) A has 16 elements, S = {(a, b) \(\in \) A\(\times\) A:a < b}; (−1, 2) and (0, 1) are two elements of S, then find the remaining elements of S.

Show that the function f : N ⟶ N given by f(x) = 2x is one-one but not onto

Show that the function f : R ⟶ R given by f(x) = cos x for all x ∈ R is neither one-one nor onto.

Find the pairs of equal sets from the following sets. A = {0}, B = {x : x > 15 and x < 5}, C = {x : x - 5 = 0}, D = {x : x² = 25}, E = {x : x is an integral positive root of the equation x² - 2x - 15 = 0}.

If a ∈ N such that aN = {a x : x ∈ N}. Describe the set 3N ∩ 7N.

Let A and B be two sets. Using properties of sets prove that A ∩ B' = Φ ⇒ A ⊂ B.