MCQs of Relations and Functions

Showing 51 to 60 out of 98 Questions

51.

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

52.

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

53.

f : R^{+} \cup {0} \to R^{+} \cup {0}, f (x) = \sqrt{x} and g : R \to R, g (x) = x^{2} - 1,

then _____ can not be obtained.

54.

If A ≠ Φ, B ≠ Φ and f : A → B is one - one function, then g : B → A exists such that gof = _____.

55.

If A ≠ Φ, B ≠ Φ and f : A → B is onto function, there exists g : B → A such that _____.

56.

If two functions f : A → B and g : B → A are such that gof = I_A , then _____.

(a)	f is many - one function and g is onto on A.
(b)	f is many - one function and g is onto on B.
(c)	f is one - one function and g is onto on B.
(d)	f is one - one function and g is onto on A.

57.

f : Z \to N, f (n) = \{\begin{cases} \begin{array}{l} 4 n; n > 0, n even \\ 4 |n| + 1; n \leq 0, n even \end{array} \\ \begin{array}{l} 4 n + 2; n > 0, n odd \\ 4 |n| + 3; n < 0, n odd \end{array} \end{cases} then f^{- 1} (3) =_____

58.

If f : Z → Z, f(x) = x - 7, then f^-1 _____.

59.

If f : R⁺ → R⁺, f(x) = x³, then f^-1 _____.

60.

If f : {1, 2, 3, ..., n} → {2, 4, 6, ..., 2n}, f(n) = 2n, then f^-1 _____.

Showing 51 to 60 out of 98 Questions