QUESTION 4 B i. Consider the piecewise function ii. iii. 6t, 12, 0 ≤t <2, t≥ 2. f(t)= Express the function f(t) in terms of unit step function. Then, show that C{f(t)} 6 6e-28 S² 82 By using convolution theorem, determine 2 C-¹ { 3² (3²-1)} Hence, based on the results in part (i) and part (ii), use Laplace transform to solve the system of differential equations da = y+ dt f(t), dy 4x + HT 0, dt. given that x=y=0 when t = 0. T

Q1 a) let f be a function defined as f(x)=3x2 + 2x². Find f(2), f(-1), f(1). b) Define functions f and g from R to R by the following formulas: f(x) = Ixl for every x belongs to R. g(x) = Vx2 for every x belongs to R Does f = g? %3D %3D %3D 2. 2,7.

2. The function f(x) is defined by the table shown below: Fill in the blanks: (a) f(_ I T(2) -3 -2 -1 0 1 2 0 1 2 345 (b) f(0) = =0 (c) f(2)= (d) f( ) = 1

6-please see attached