9709/MayJune/12/2010/Q11

The function f : x → 4 − 3 sin x is defined for the domain 0 ≤ x ≤ 2pi.

(i) Solve the equation f(x) = 2. [3]

(ii) Sketch the graph of y = f(x). [2]

(iii) Find the set of values of k for which the equation f(x) = k has no solution. [2]

The function g : x → 4 − 3 sin x is defined for the domain 1/2 ≤ x ≤ A

(iv) State the largest value of A for which g has an inverse. [1]

(v) For this value of A, find the value of g⁻¹(3). [2]

Solution:

i)

ii)

f(x) = 3 sin x

f(x) = -3 sin x

f(x) = 4 - 3 sin x

iii)

iv)

v)

Reference: PYQ - May/June 2010 Paper 12 Q11