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Let f(x) = 3x + 2, and let g(x) = f(f(x)) - f(f(f(x)). If the domain of g is 0 <= x <= 2, compute the range of g.

 Jan 30, 2022
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g(x) = f(f(x)) - f(f(f(x)))

= f(3x+2) - f(f(3x+2))

= 3(3x+2) + 2 - f(3(3x+2) + 2)

= 9x + 8 - f(9x + 8)

 = 9x + 8 - (3(9x + 8) + 2)

= 9x + 8 - (27x + 26)

= -18x - 18

 

x is in [0, 2]

g(x) is in [-54, -18]

 Jan 30, 2022

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