Use the rules of the algebra of functions to combine the following functions by finding (1) (f + g)(x),

(2) (f – g)(x), (3) (f · g)(x), and (4) (f ÷ g)(x).

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(a) f(x)=4x-5, g(x) = 7x - 3 (1) (f+g)(x) = f(x) + g(x) = (4x-5)+(7x-3)=11x8 (fg)(x) = f(x)g(x) = (4x-5) (7x-3)=-3x-2 - =(4x-5) (7x-3)=28x-47x + 15 (3) (fg)(x) = f(x) g(x) 4x-5 (4) (fg)(x) = f(x) = g(x) = 7x-3 (b) f(x) = x+3, g(x) = 4x-7 # (1) (f+g)(x) = (x+3)+(4x-7)= x+4x-4 (fg)(x) = (x+3) - (4x-7)= x-4x+10 (3) (fg)(x) = (x+3) (4x-7)=4x-7x + 12x - 21 (4) (fg)(x) = 2+3 4x-7 3 (c) f(x) = g(x) 4 = (x 0,-5) x+5 (1) (f+g)(x) = (2) (f-g)(x) (3) (fg)(x) = = (4) (fg)(x) = 3 - =- 3-x 3-X 4 3(x+5)+4x 7x+15 + = x+5 - 4 x+5 = = x(x+5) r2+5 3(x+5)-4x 15-x = x(x+5) x2+5x 4 12 12 = = x x+5 x(x+5) r2+5x 3-x 4 3 x+5 3x+15 = = x+5 x 4 4.x