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Find the inverse function of f. State the domain and range of both f and f-1. Sketch both, the functions, and its inverse on the same axes to show the symmetry about the line y = x. 7. f (x) = x2 +2, x20 8. f (x) = Vx+3 Answer : 7. f-1(x) = Vx- 2, Df = Rf-1 = [0, co), Rf = Df-1 = [2, 00) 8. f (x) = x2 -3, Df = Rf-1 = [-3, 00), Rf = Df-1 = [0, 00)TUTORIAL 4 : CHAPTER 2 OPERATIONS ON FUNCTIONS Find f + g,f - g, fg,f /g and state the domain of each. 1. f(x) = 2x2 -x, g(x) =x2 -4 3. f (x) = V4 -x, g(x) = vx+3 2. 2x + 3 f (x) =. x - 4 4. 2x X g (x) = f ( x) = g(x) = x - 4 3x + 2 x - 4 x + 5 Answer: Domain f + g, f - g,f . g: Domain f / g: 1. (-00, 00) (-00, -2) U (-2,2) U (2, 00) 2. (- 0o, - 2) U (- 3,4 ) U(4, 00) ( - 0o , - 3 ) U ( - 3, 4) U(4, 00 ) 3. [-3, 4] (-3, 4] 4. (-00, -5) U ( - 5, 4) U ( 4, 00 ) (-00, -5) U (-5, 0) U (0,4) U (4, 00)INVERSE FUNCTIONS Find the inverse function of f. State the domain and range of both f and f '1. 1. f(x)=x21, x50 2.. f(x)=x2+2x3, xsl 3- f(x) = \\/x + 5 4. f(x) = (3 x)2, x 2 3 5. f(x)=3(x4)2, x34 6. f(x)=x2+4x, 9532 Inverse | f (x) f '1(x) Answer Function Domain Range Domain Range m COMPOSITE FUNCTIONS Find the composite function fog and go f, and state its domains. 1 . f ( x ) = x2 +1, g(x ) = x-1 3. 1 f ( x) = - g(x) = X x +1 2. f (x) = Vx -2, g(x) =Vx+5 4. 1 f ( x ) = g ( x) = x+2 x - 1' Answer: Domain fog: Domain go f : 1. (-00, 00 ) (-00, 00) 2. [-1, 00) [27,00) . (-00, -1) U (-1, 00) (-00, -1) U (-1, 0) U (0, 00) 4. (-00, -1) U (-1, 00) (-00, 1) U (1,00)