Discrete Mathematics Questions and Answers for Entrance exams 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
Answer: b
Clarification: 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) x2
d) none of the mentioned
Answer: b
Clarification: 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
Answer: b
Clarification: 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
Answer: b
Clarification: y = 3x-5, x = (y+5)/3, f -1(x) = (x+5)/3.
5. For some bijective function inverse of that function is not bijective.
a) True
b) False
Answer: b
Clarification: If f(x) is a bijection than f -1(x) is also a bijection.
6. f(x) is a bijection than f -1(x) is a mirror image of f(x) around y = x.
a) True
b) False
Answer: a
Clarification: 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) = x2 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
Answer: c
Clarification: 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) x2
d) none of the mentioned
Answer: a
Clarification: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
Answer: b
Clarification: Inverse of a function is the mirror image of function in line y = x.
10. Let f(x) = x then number of solution to f(x) = f -1(x) is zero.
a) True
b) False
Answer: b
Clarification: Since inverse of a function is the mirror image of function in line y = x, therefore in this case infinte solution will exist.