Section 6.1 (Sullivan, 8th ed.) MAC1140, MAC11476-1: Composite FunctionsA composite function is obtained by substituting one function into another function;(f g)(x) = f(g(x)), read f composed with g(x), means that every x in function f isreplaced with the g function. To evaluate a composite function, (f g)(n), evaluatefunction g for n, then evaluation function f for g(n).[1]x -3-2 -1 0 1 2 3 Find:f(x)119 7 5 3 1 -1(f g)(1)g(x)-8-3 0 1 0 -3 -8(g f)(3)2. Graph the points: y = f(x) = {(-1, 1), (1, -1), (2, -2), (4, 0), (5, 1), (6, 2), (7, 3), (8,4)} and y = g(x) = {(-1, 3), (0, 5), (1, 4), (3, 1), (4, 2), (5, 4), (6, 5), (7, 5)} Graph f(x) as an absolute value segment and g(x) as a polynomial curve.a. Find (f g)(5) b. Find (g f)(-1)Given f(x) = 2x2 – 3 and g(x) = x-3 15, find the composite and state its domain: Domain of f(x): (-∞, ∞) Domain of g(x): x ≥ 5[3] (f g)(x) and (f g)(3) [4] (g f)(x) and (g f)(3) [5] (f f)(x) and (f f)(-2)Section 6.1 (Sullivan, 8th ed.) MAC1140, MAC1147Given ( )-=-xf xx2 12and ( )+=-42 5xg xx, find:[9] (f g)(3) [10] (g f)(3)Find the functions f and g so that f g = H11. H(x) = ( )x+32112. H(x) = 2x2 + 313. If f(x) = 3x2 – 7 and g(x) = 2x + a, find a so that the graph of f g crosses the y-axis at 140.Section 6.1 (Sullivan, 8th ed.) MAC1140,
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