# Let f , g, h be functions from R to R .Show that (f + g)oh = foh + goh, (f .g)oh = ( foh).( goh)

**Solution:**

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B.

According to the given problem,

(f + g)oh = foh + goh

LHS = [(f + g)oh] (x)

= (f + g) [h (x)]

= f [h (x)] + g [h (x)]

= ( foh)(x) + goh (x)

= {(foh) + (goh)}(x) = RHS

Therefore,

{(f + g )oh} (x) = {(foh) + (goh)}(x) for all x ∈ R

Hence,

(f + g)oh = foh + goh

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

LHS = [(f .g)oh] (x)

= (f .g) [h ( x)] = f [h (x)] .g [h (x)]

= (foh)(x).(goh)(x)

= {(foh).(goh)} (x) = RHS

Therefore,

[(f .g)oh] (x) = {(foh).(goh)} (x) for all x ∈ R

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

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.3 Question 2

## Let f , g, h be functions from R to R .Show that (f + g)oh = foh + goh , (f .g)oh = ( foh).( goh)

**Summary:**

Given that f , g, h be functions from R to R. Here we have shown that {(f + g )oh} (x) = {(foh) + (goh)}(x) for all x ∈ R and [(f .g)oh] (x) = {(foh).(goh)} (x) for all x ∈ R