Compute the compositions fgx ffx and gfx in each case fx x2

Compute the compositions f(g(x)), f(f(x)) and g(f(x)) in each case. f(x) = x^2, g(x) = x +3 f(g(x)) = __ f(f(x)) = _____ g(f(x)) = _____ f(x) = 1/x, g(x) = Squareroot x f(g(x)) = ____ f(f(x)) = ______ g(f(x)) = ________ f(x) = 4x + 7, g(x) = 1.4(x-7) f(g(x)) = ___ f(f(x)) =__ g(f(x)) = _________

Solution

a)   f(x) = x^2,     g(x) = x + 3

   f(g(x)) = (x + 3)^2 =x^2 + 6x + 9

    f(f(x)) = (x^2)^2 =x^4

    g(f(x)) = x^2 + 3

b)   f(x) = 1/x,     g(x) = x^1/2

   f(g(x)) = 1/x^1/2 = x^-1/2

    f(f(x)) = 1/(1/x) = x

    g(f(x)) = (1/x)^1/2 = x^-1/2

c) f(x) = 4x + 7,     g(x) = (x - 7)/4

   f(g(x)) = (x - 7) + 7 = x

    f(f(x)) = 4(4x + 7) + 7 = 16x + 35

    g(f(x)) = (4x + 7 - 7)/4 = x