Ty D. answered • 10/08/18

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Essentially we are plugging equations into one another based on what's specified in the problem and then simplifying the expression. Each time we will use

f(x) = 1/x and/or g(x) = 2x + 8

g((f(x)) = g(1/x)

g(1/x) = 2 (1/x) + 8 = 2/x + 8

g(f(x)) = 2/x + 8

**Here I am plugging the equation for f(x) = 1/x into the equation for g(x) in place of the x. I follow the same process for the other problems using the the given equations.

f(f(x)) = f(1/x)

f(1/x) = 1/ (1/x) = x

f(f(x)) = x

g(g(x)) = g (2x+8)

g(2x+8) = 2 (2x+8) +8 = 4x + 16 + 8 = 4x + 24

g(g(x)) = 4x + 24

Trey C.

10/08/18