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Let f, g, and h be functions from R to R...

Let f, g, and h be functions from R to R. Show that
`(f cdot g) o h = (foh) cdot (goh)`

Text Solution

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`[ (f cdot g) o h] (x) = (f cdot g) (h (x))`
`= f(h(x)) cdot g(h (x))`
`(f o h)(x) cdot (g o h)(x)`
`= [(foh) cdot (goh)](x)`, for all `x in R`
Thus, `(f cdot g)` o h = (foh) `cdot` (goh)
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