Answer :

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

Let us consider ((f + g)oh)(x) = (f + g)(h(x))


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


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


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


Then, ((f + g)oh)(x) = {(foh) +(goh)}(x) x ϵ R


Therefore, (f + g)oh = foh + goh.


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


Let us consider ((f.g)oh)(x) = (f.g)(h(x))


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


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


= (fog)(x).(goh)(x)


= {(fog).(goh)}(x)


Then, ((f.g)oh)(x) = {(fog).(goh)}(x) x ϵ R


Therefore, (f.g)oh = (fog).(goh)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

| Let * be a binaMathematics - Board Papers

Find the idMathematics - Board Papers

Let f : A Mathematics - Exemplar

Show that the binMathematics - Board Papers

Determine whetherRD Sharma - Volume 1

Fill in theMathematics - Exemplar