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
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