Which of these pairs of functions are inverse functions?

  see below

Step-by-step explanation:

You can attack this several ways. One is to work through f(g(x)) in each case and see if the result is x.

Another is to use a graphing calculator to evaluate y=f(g(x)) to see if the result is the line y=x.

Yet another way to work this is to pick a convenient value for x and evaluate f(g(x)) or g(f(x)). Here, we'll show this last case.

  A: f(1) = 2^0 +1 = 2; g(2) = log2(2-1) -1 = -1 . . . . g(f(1)) = -1, not 1 ⇒ not inverses

  B: f(2) = 1/2(ln(1) -1) = -1/2; g(-1/2) = 2e^(0) = 2 . . . g(f(2)) = 2 ⇒ inverses

  C: f(e) = 4ln(e^2)/e^2 = 8/e^2; g(8/e^2) = e^1 = e . . . g(f(e)) = e ⇒ inverses

  D: f(10) = 10^0-10 = -9; g(-9) = log(1) -10 = -10 . . . g(f(10)) = -10, not 10

      ⇒ not inverses

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The second and third pairs of functions are inverses.

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step-by-step explanation: