Question: Compute the compositions f(g(x)), f(f(x)) and g(f(x)) in each case. (a) f( x) = x2, g(x) = x+2 Ag(x) ) = x- + 4x+4 f(

Compute the compositions f(g(x)), f(f(x)) and g(f(x)) in each case. (a) f( x) = x2, g(x) = x+2 Ag(x) ) = x- + 4x+4 f( f(x) ) = X g(f(x)) = x+2 (b) f(x) = 1/x, g(x) = vx Alg (x) ) = f( f ( x ) ) = g(f(x) ) = (c) f( x) = 9x + 4, g(x) = _(x -4) Alg (x) ) = f ( f ( x ) ) = g(f(x)) = (d) f(x) = 6x2 + 3, g(x) = x -2 Alg(x)) = 6x2 - 4x + 57 X F(f ( x ) ) = 216x* + 216x2 + 57 g(f(x)) = 6x-+ 1 (e) f(x) = 4x3 - 2, g(x) = \\ 2x + 4 Alg(x)) = 8x + 14 f( f ( x ) ) = 256x" - 256x + 64x - 34 X g(f(x)) = 2x (f) f(x) = 9x + 1, g(x) = x3 Alg(x)) = 9x* + 9 X f( f ( x ) ) = 81x + 90 X g(f(x) ) = 729 (x + 1)3 X

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