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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) - CBSE (Commerce) Class 12 - Mathematics

ConceptComposition of Functions and Invertible Function

#### Question

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

(f + g)oh = foh + goh

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

#### 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)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 2 | Page no. 18

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Solution Let F, G And H Be Functions From R To R. Show that (F+G)Oh=Foh+Goh (F.G)Oh=(Foh).(Goh) Concept: Composition of Functions and Invertible Function.
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