This set of Discrete Mathematics Questions and Answers for Entrance exams focuses on “Inverse of a Function”.

1. For an inverse to exist it is necessary that a function should be :

a) injection

b) bijection

c) surjection

d) none of the mentioned

View Answer

Explanation: Inverse exist only for those functions which are one one and onto.

2. If f(x) = y then f ^{-1}(y) is equal to :

a) y

b) x

c) x^{2}

d) none of the mentioned

View Answer

Explanation: On giving inverse, image the function returns preimage thus f

^{-1}(y) = x.

3. A function f(x) is defined from A to B then f ^{-1} is defined :

a) from A to B

b) from B to A

c) depends on the inverse of function

d) none of the mentioned

View Answer

Explanation: Inverse associate each element in B with corresponding element in A.

4. If f is a function defined from R to R , is given by f(x) = 3x – 5 then f ^{–1}(x) is given by:

a) 1/(3x-5)

b) (x+5)/3

c) does not exist since it is not a bijection

d) none of the mentioned

View Answer

Explanation: y = 3x-5, x = (y+5)/3, f

^{-1}(x) = (x+5)/3.

5. State whether the given statement is true or false

For some bijective function inverse of that function is not bijective.

a) True

b) False

View Answer

Explanation: If f(x) is a bijection than f

^{-1}(x) is also a bijection.

6. State whether the given statement is true or false

f(x) is a bijection than f ^{-1}(x) is a mirror image of f(x) around y = x.

a) True

b) False

View Answer

Explanation: Inverse of a function is the mirror image of function in line y = x.

7. If f is a function defined from R to R , is given by f(x) = x^{2} then f ^{–1}(x) is given by:

a) 1/(3x-5)

b) (x+5)/3

c) does not exist since it is not a bijection

d) none of the mentioned

View Answer

Explanation: It is not a one one function hence Inverse does not exist.

8. For any function fof ^{-1}(x) is equal to ?

a) x

b) 1

c) x^{2}

d) none of the mentioned

View Answer

Explanation:Compostion of a function with its inverse gives x.

9. The solution to f(x) = f ^{-1}(x) are :

a) no solutions in any case

b) same as solution to f(x) = x

c) infinite number of solution for every case

d) none of the mentioned

View Answer

Explanation: Inverse of a function is the mirror image of function in line y = x.

10. State True or False.

Let f(x) = x then number of solution to f(x) = f ^{-1}(x) is zero.

a) True

b) False

View Answer

Explanation: Since inverse of a function is the mirror image of function in line y = x, therefore in this case infinte solution will exist.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

To practice all areas of Discrete Mathematics for Entrance exams, __here is complete set of 1000+ Multiple Choice Questions and Answers__.