2.For this question, we define the rules f(x)=e^1/x, g(x)= sin(2x) cos(3x) and h(x) = ?(x + 2).(a) Write out the following explicitly. You do not need to give a domain and codomain.i. (f ? h)(x)

ii. (h ? g)(x)iii. g(x²)iv. f(x + y)(b) For the rule f defined above, give a domain and the corresponding range.(c) What is the range of the function k : R ? R, where k(x) = - 3/2sin ( 2x - 3?/4 ) + 7/3.

3.Evaluate the following limits, or explain why they do not exist. Make sure to show all working.

(a) lim (2x²-x-3)/(x²-1) x??1

(b) lim (2x²-x-3)/(x²-1)

x???(c) lim |x ? 2| / x-2 x?2(d) lim. sin(x²)/x x?0

4. Let a, b ? R. Consider the piecewise function f : R ? R defined by ? (x ? ?)² - 1 x

??2 cos(x) + a x > ?Find all values of a and b which make f(x) continuous on R.

5. For each of (a)-(d) below, decide whether the statement is True or False. If True, explain why.If False, give a counterexample.(a) ?(x²) =(?x)² for all x ? R.(b) If A ? B = A for two sets A and B, then A = B.(c) For some a ? R, if f(a) is not defined, then lim f(x) does not exist.

x?a(d) The equation x² + 2y² = 3 defines y as a function of x on R.

2. For this question, we define the rules f(x) = ex, g(x) = sin(2x) cos(3x) and h(x) = vx + 2. (a) Write out the following explicitly. You do not need to give a domain and codomain. i. (foh)(r) iii. g(x?) ii. (hog)(x) iv. f(a + y) (b) For the rule f defined above, give a domain and the corresponding range. (c) What is the range of the function k : R - R, where k(x) = 3 - sin + 091 [12 marks]2. For this question, we define the rules f(x) = ex, g(x) = sin(2x) cos(3x) and h(x) = vx + 2. (a) Write out the following explicitly. You do not need to give a domain and codomain. i. (foh)(r) iii. g(x?) ii. (hog)(x) iv. f(a + y) (b) For the rule f defined above, give a domain and the corresponding range. (c) What is the range of the function k : R - R, where k(x) = 3 - sin + 091 [12 marks]