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Question

For function f(x)=3x-2 and g(x)=5x+1, find (f o g)(x) and (g o f)(x)

Answer 1

f comp g = 3(5x+1) - 2 = 15x +3 - 2 = 15x + 1 = J(x)

g comp f = 5(3x-2) + 1 = 15x - 10 + 1 = 15x - 9 = K(x)

Now we check it with a test value: pick x=0

f(0) = -2 and g(0) = 1

g(f(0)) = g(-2) = -10 + 1 = -9

Note that K(0) = -9 as well

f(g(0)) = 1; note that J(0) =1 as well