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- 1. 17) express the given function h as a composition of two functions f and g so that h(x)=(f*g)(x), where one of the functions is 5x-4 h(x)=(5x-4)^3 a. f(x)= b.g(x)= 18) find f(g(x)) and g(f(x)) and determine wether the pair of functions f and g are inverses of each other f(x)=6x and g(x)= x over 6 a. f(g(x))= b. g(f(x))= c. inverse or not? 19) if the function is one-to-one, find its inverse g(x)= /x-3, x>3 a. is the function one-to-one? b. function undefined or g^-1(x)=Â Â Â Â Â Â Â Â , x>0
- 2. Solution 17) a )f(x) = x^3 b ) g(x) = 5x-4 18) a ) f(g(x)) = f(x/6) = x b ) g(f(x)) = g(6x) = x c) yes inverse because f(g(x)) = g(f(x)) 19) assuming g(x) = 1 /(x-3) x> 3 a ) yes the function is one - one because f(x) is decreasing function completely. b ) g^-1(x) = y x = g(y) = 1 /(y-3) xy - 3x = 1 y = (1 + 3x) /x y = 1/x + 3 g^-1(x) = 1/x + 3