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10 November, 01:16

If f (x) = x + 8 and h (x) = 3x - 3, find a function g such that g ∘ f = h.

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  1. 10 November, 01:57
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    Hello:

    If f (x) = x + 8 and h (x) = 3x - 3,

    g ∘ f = h

    g ∘ (f ∘ f ^-1) = h ∘ f ^-1 (proprety associative)

    but;

    (f ∘ f ^-1) = x

    g ∘ x = g

    g (x) = (h ∘ f ^-1) (x)

    calculate : (f ^-1) (x)

    f (x) = x + 8

    x = f (x) - 8

    so : (f ^-1) (x) = x - 8

    g (x) = (h ∘ f ^-1) (x) = h ((f ^-1) (x)) = h (x - 8) = 3 (x - 8) - 3

    g (x) = 3x - 27
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