If f: Z → Z, f = x + 2 and g:

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If f: Z → Z, f = x + 2 and g: Z → Z with gof = I_z, then g is

Options:

x + 2

x – 2

x – 1

x + 1

Correct Answer:

x – 2

Explanation:

gof = I_z⇒ (gof)(x) = x for all x ∈ Z so that g(f(x)) = x

or g(x + 2) = x ⇒ g(x) = x - 2, x ∈ Z.

Hence (B) is the correct answer.