Exercise 8.6.6. Fill in the blanks of the following proof to show that function composition is associative. PROOF. Suppose f :X → Y, g :Y → W, and h : W → Z. Then ho (go f)(x) = h((g o f)(x)) = _<1>. and (h og) o f(x) = (h o g)(_<2> _) = _< 3> . Since the two right-hand sides are equal, it follows that ho (go f)(x) (hog) o f(x); in other words function composition is associative.
Exercise 8.6.6. Fill in the blanks of the following proof to show that function composition is associative. PROOF. Suppose f :X → Y, g :Y → W, and h : W → Z. Then ho (go f)(x) = h((g o f)(x)) = _<1>. and (h og) o f(x) = (h o g)(_<2> _) = _< 3> . Since the two right-hand sides are equal, it follows that ho (go f)(x) (hog) o f(x); in other words function composition is associative.
Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:Exercise 8.6.6. Fill in the blanks of the following proof to show that
function composition is associative.
PROOF. Suppose f : X → Y, g :Y →W, and h : W –→ Z. Then
ho (go f)(r) = h((go f)(x)) = <1> ,
and
(h o g) o f(x) = (h o g)(_< 2 > _) = _<3> .
Since the two right-hand sides are equal, it follows that ho (go f)(x) =
(h o g) o f(x); in other words function composition is associative.
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