J's answer to Loui's Philippines question.
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One example of a one-to-one function would be : f(x) = eˣ
Replace f(x) with x and replace x with g(x)
x = eᵍ⁽ˣ⁾
Take ln on both sides,
ln x = g(x)
Then,
(f○g)(x)= eˡⁿ⁽ˣ⁾ = x
(g○f)(x) = ln(eˣ) = x lne = x(1) = x
(Proved)
Replace f(x) with x and replace x with g(x)
x = eᵍ⁽ˣ⁾
Take ln on both sides,
ln x = g(x)
Then,
(f○g)(x)= eˡⁿ⁽ˣ⁾ = x
(g○f)(x) = ln(eˣ) = x lne = x(1) = x
(Proved)
Date Posted:
3 years ago
thanks
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