Solve each questions with complete explanation:

PROBLEM 4.16 If f and g be two linear func- tions from [-1, 1] onto [0, 2] and Q : R - {-1, 1} f (x) R be defined by o(x) = , then show that ob off g(x) Q (0(x) ) + $ $ 3 ) )I 2 2. 18094PROBLEM 4.22 Let f (x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y - 2x) for all x, y. Show that g(x) = f(2* , 0) is a periodic function with period 12.PROBLEM 4.24 Consider a function f(x) = x +a ,XER - {1} where a is a real constant. If X - 1 f is not a constant function, find the following (i) f-1, is it exist (ii) the range of f (iii) f f (f(x) )PROBLEM 4.29 Let f: R- 12) -> R be a func- tion satisfying the following functional equation, 2x + 29 2f(x) + 3f = 9 X A 08 + XOOI X - 2 R- {2}. Determine f(x).PROBLEM 4.32 Suppose that f(x) is a func- tion satisfying (f(m + n) - f(m)| s - for all posi- m tive rational number m and n. Prove that, for all natural numbers k, K [|f ( 2 * ) - f(21 )/ s k (k - 1 ) 2 i=1PROBLEM 4.8 Find the range of the follow- ing functions andT MOITU.108 V2x +1 (i) y = cos -1 [xy Lax seusosd (0) X - +1 (ii) y = log, (2 - 10g 52 (16 sin x + 1))