4. Determine the domain of the following function. g (x) = sin(x + a) + b 5. For the following nested function, find f (g(4)) by writing f(g(x)) in the simplest form and substituting in x=4. f(x) = x'+8x - 2 and g(x) =x2 6. For the following set of functions, find the point where they intersect. f(x) = 3x - 2 and g(x) = -3x + 4. 7. For the function f(x) = x2+ 3x - 2, write the function which would have the same graph, but shifted c units right.9. A DC electric motor is connected to a wheel via a gearbox. The aim is to find when to engage the gear so that the torque at the wheel is always the largest possible. On its own, the motor generates a torque M () (in Nm) that depends on the rotation speed (in rpm) of the motor shaft: M(2) = 0.3 600 The torque (w) exerted at the wheel depends on the rotation speed w of the wheel, and on whether the gear is engaged: To(w) = M(w), if the gear is not engaged, TI(w ) = 21 if the gear is engaged. (a) Write explicit expressions for To(w) and T1 (w) as functions of w given the definition of M (Q). (b) Plot the two functions you found in (a) on a same graph for positive values of w. (c) Find the optimal gear shifting point w* that ensures that the torque T(w) is always as large as possible. Hint: Look for a graphical solution first by using the graph from Part (b)