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Let F, G And H Be Functions From R To R. Show that (F+G)Oh=Foh+Goh (F.G)Oh=(Foh).(Goh) - Mathematics

Let fg and h be functions from to R. Show that

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

`(f.g)oh = (foh).(goh)`

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Solution

To prove:

(f + g)oh = foh + goh

Consider:

`((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)           ∀x ∈ R

Hence (f + g)oh =  foh + goh 

To prove

`(f.g)oh = (foh).(goh)`

Consider

`((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)`   ∀x ∈ R

Hence `(f.g) oh = (foh).(goh)`

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APPEARS IN

NCERT Class 12 Maths
Chapter 1 Relations and Functions
Q 2 | Page 18
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