• NCERT Chapter
Question 3

# Find gof and fog, if(i) f(x) = | x | and g(x) = | 5x – 2 | (ii) f(x) = 8x3 and g(x) = x1/3 .

(i) f(x) = | x | and g(x) = | 5x – 2 | (ii) f(x) = 8x3 and g(x) = x1/3 ">

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:- 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:-

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 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.

• 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.