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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 1.`(f+g)oh=foh+goh
2. (f.g)oh= (foh).(goh)`

Text Solution

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(i) `((f+g)oh)(x) = (f+g)(h(x))`
`=f(h(x))+g(h(x))`
`=(foh)(x)+(goh)(x)`
`=[(foh+goh)](x)`
`:. ((f+g)oh)(x) = [(foh+goh)](x)`
`=>((f+g)oh) = (foh+goh)`

(ii)`((f*g)oh)(x) = (f*g)(h(x))`
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