"Let f : X → Y , g : Y → Z and

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

"Let f : X → Y , g : Y → Z and h : Z → s are functions , then

Options:

ho(gof) and (hog)of are not defined

ho(gof) and (hog)of are well defined and ho(gof) = (hog)of

ho(gof) may not be equal to (hog)of

None of these

Correct Answer:

ho(gof) and (hog)of are well defined and ho(gof) = (hog)of

Explanation:

$LHS = hο(gοf)(x)$

$=h(gof(x))=h(g(f(x)))$

$RHS=(hog)of(x)$

$=hog(f(x))=h(g(f(x)))$

$LHS=RHS⇒ho(gof)(x)=(hog)of(x)$