Could I please have some help with this question

(a) Channelle is asked to examine the properties of the function k : IR - R defined by k(x) = arccos ( sin(cz)) , where c is a non-zero constant. Channelle takes a shortcut and uses Maple: > k := x -> arccos (sin (c*x) ) : > simplify (diff (k (x) , x, x) ) ; 0 Channelle concludes that k() must be of the form k(x) = ar +b, where a and b are constants. Finally, Channelle reasons that the Maple output > k (Pi/2/c) ; k(-3*Pi/2/c) ; must mean that a = 6 = 0 and, hence, k(z) = 0 for all x E R. In order to verify this assertion, Channelle uses Maple once again: > k(-Pi/2/c) ; Channelle is now totally confused and needs your help. Explain carefully why Channelle's reasoning is incorrect. Essay box advice: In your explanation, you don't need to use exact Maple syntax or use the equation editor, as long as your expressions are sufficiently clear for the reader. For example, you can write . k(I) as 4(x)', as 'pi/2", arccos ( sin(cr)) as 'arccos( sin(c x) )' = Q ESHation A - A-IX BIUSXX Styles Font . . . Words: 0(b) Having realised that Maple outputs can be deceptive, Channelle now considers a more general function f : R - R given by f(Ex) = arccos (7p sin(cz)) , where p is a real constant. Channelle is interested in the answers to two questions. Syntax advice: Enter your answers using interval notation. For example, (-4,7) should be written as (-4,7) (15, 38] should be written as (15,38] Firstly, for which values of p is D = R the maximal domain of f? Answer: The maximal domain is D = R if and only if p E Secondly, for which values of p is f (defined and) differentiable on D = R? Answer: f is differentiable on D = R if and only if p e