MCQs of Relations and Functions

Showing 61 to 70 out of 145 Questions

61.

If f : R \to R, f (x) = |x|, g : R \to R, g (x) = x^{2}

then. _____

62.

f : [- 1, 1] \to [- 1, 1], f (x) = x |x| is_____

63.

If f : R^{+} \to R^{+}, f (x) = x^{3}, g : R^{+} \to R^{+}, g (x) = x^{\frac{1}{3}},

then _____.

64.

Let S be the relation on the set A={5,6,7,8}, S={(5,6), (6,6), (5,5), (8,8), (5,7), (7,7), (7,6)} then _____

(a)	S is reflexive and symmetric but not transitive
(b)	S is reflexibe and transtive but not symmetric
(c)	S is symmetric and transtive but not reflexive
(d)	S is an equivalence relation

65.

If f : R^{+} \to R, f (x) = (3 - x^{3})^{\frac{1}{3}}, then f o f

_____.

66.

I f f : R \to R, f (x) = [x], g : R \to R, g (x) = s i n x, h : R, h (x) = 2 x, t h e n h o (g o f) =_____

67.

If f : R - {- 1} \to R - {- 1}, f (x) = \frac{1 - x}{1 + x},

then fof = _____.

68.

If f : R \to R, f (x) = \{\begin{matrix} 1, & x > 0 \\ 0, & x = 0 \\ - 1, & x < 0 \end{matrix} and g : R \to Z, g (x) = [x]

, then _____.

69.

I f f : R \to (- 1, 1), f (x) = \frac{- x |x|}{1 + x^{2}} t h e n f^{- 1} (x) =_____

70.

If f : Z \to Z, f (n) = 5 n and g : Z \to Z, g (n) = \{\begin{matrix} \frac{n}{5}, & if 5 | n \\ 0, & otherwise \end{matrix},

then _____.

(a)	gof = I_Z, fog = I_Z
(b)	gof = I_Z, 5Ιn, (gof) (n)= 0 otherwise
(c)	fog = I_Z, 5Ιn, (fog) (n)= 0 otherwise
(d)	fog = gof = I_Z, 5Ιn, (fog) (n)= (gof) (n) = 0 otherwise

Showing 61 to 70 out of 145 Questions