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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+g)oh=foh+goh(fg)oh= (foh)(goh)`

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`{(f+h)oh} (x) = (f+g) {h(x)}`
`" " = f{h(x)} + g{h(x)}`
`" " = (foh)(x) + (goh)(x)`
`" " = {(foh) + (goh)}(x)`
`therefore " " (f+g)oh = (foh)+ (goh)` Hence proved.
Again `{(f*g)oh} (x) = (f*g){h (x)}`
`" " = f{h(x)} *g{h(x)}`
`" " = {(foh) (x)} *{(goh)(x)}`
`" " = {(foh)*(goh)} (x)`
`therefore " " (f*g)oh = (foh) *(goh)` Hence Proved
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