Questions on Functions and Their Properties with Answers

Practice Questions on Functions and Their Properties with Answers

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Questions on Functions and Their Properties with Answers

Q1. The number of distinct real roots of the equation x9+x7+x5+x3+x+1=0 is

(a) 1
(b) 3
(c) 5
(d) 9

Q2. Limit of the function (1-1/n2)n where n → ∞ is equal to

(a) 1
(b) e-1/2
(c) e-2
(d) e-1

Q3. Consider the functions f, g : Z→ Z defined by f(n) = 3n + 2 and g(n) = n2 – 5

(a) Neither f  and g is a one-to-one function
(b) Ths function f is one-to-one, but not g
(c) Ths function g is one-to-one, but not f
(d) Both f and g are one-to-one functions

Q4. Let a,b,c,d be rational number with ad – bc ≠ 0. Then the function f : R\Q → R defined by f(x) = (ax+b)/(cx+d)

(a) onto but not one-one
(b) one-one but not onto
(c) neither one-one nor onto
(d) both one-one and onto

Q5. Let f:(0,∞) → R be the function defined by f(x) = ex/xx. Then the limit of f(x) where x→∞

(a) does not exist
(b) exists and is 0
(c) exists and is 1
(d) exists and is e

Q6. The correct value of limit of the f(x) = x/√(1-cosx) where x→0

(a) does not exist
(b) is √2
(c) is  -√2
(d) is 1/√2

Q7. If X and Y are two non-empty finite sets and f:X→Y and g:Y→X are mappings such that g o f : X→X is a surjective (i.e, onto) map, then

(a) f must be one-to-one
(b) f must be onto
(c) g must be one-to-one
(d) X and Y must have the same number of elements

Q8. Let P(x) be a non-constant polynomial such that P(n) = P(-n) for all n∈N. Then P'(0)

(a) Equals 1
(b) Equals 0
(c) Equals -1
(d) Can not be determined from the given data

Q9. If f(x) = 1/(1-x) , g(x) = f[f(x)] and h(x) = f[g(x)], then what is f(x)g(x)h(x) equal to ?

(a) -1
(b) 0
(c) 1
(d) 2

Q10. What is the value of Limit of f(x) = (xy – yx)/(xx – yy) ?

(a) (1+lny)/(1-lny)
(b) (1-lny)/(1+lny)
(c) (-1+lny)/(1+lny)
(d) (-1-lny)/(1-lny)

Q11. If D is the set of all real x such that f(x) = 1 – e(1-x)/x is positive, then what is D equal to ?

(a) (-∞,0) ∪ (1,∞)
(b) (-∞,0) ∪ [1,∞)
(c) (1,∞)
(d) (-∞,1)

Q12. Assertion (A) : ex cannot be expressed as sum of even and odd functions.
Reason (R) : ex is neither even nor odd function

(a) Both A and R are individually true but R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

Q13. Let f:R→R define g:R→R by g(x) = f(x)[f(x) + f(-x)]. Then

(a) g is even for all f
(b) f is odd for all f
(c) g is even if f is even
(d) g is even if f is odd

Q14. The limit of function  f(x) = (4x + 5x)1/x where x → ∞ is equal to

(a) 4
(b) 5
(c) e
(d) 5e

Q15. Which one of the following function is not well defined ?

(a) √(1 + sinx)
(b) √(5sec2x – 4)
(c) √(3 – cos2x)
(d) √(x4 + x2 + 1/100)

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