• NCERT Chapter
Question 2

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

To prove:

(f + g)oh = foh + goh To Prove:

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

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Let A = R – {3} and B = R – {1}. Consider the function  f : A → B defined by . Is f one-one and onto? Justify your answer.

• Q:- Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
• Q:-

Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

• Q:- Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = { (a,b) ; |a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
• Q:- Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b2} is neither reflexive nor symmetric nor transitive.
• Q:-

Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.