Function or Mapping

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

A function `f : \mathbb{R} -> \mathbb{R}` is defined by `f(x)=(x-1)(x-2)`. Then which of the following is true? (a) function is one-one but not onto, (b) function is onto but not one-one, (c) function is neither one-one nor onto, (d) function is one-one and onto.

Question No: #2

Let `\mathbb{Z}` be the set of all integers and a mapping `f : \mathbb{Z} \to \mathbb{Z}` is defined by `f(x) = x^2`. Then `f^{-1}(-4)` is -- (a) `{2}`, (b) `{-2}`, (c) `{-2,2}`, (d) `\phi`

Question No: #3

Let `\mathbb{I}` be the set of all integers. A function `f : \mathbb{I} -> \mathbb{I}` is defined by `f(x)=3x^2-14x+10`. Then find `f^{-1}(2)`

Question No: #4

Show that the modulus function `f : \mathbb{R} \rarr \mathbb{R}`, given by `f(x) = |x|` is neither one-one nor onto, where $|x| = \begin{cases} x, & \text{when } x\ge0 \\ -x, & \text{when } x\lt0 \end{cases}$

Question No: #5

Show that the mapping `f : \mathbb{N} \rarr \mathbb{N}` defined by `f(x)=2^x` is injective, but not surjective mapping.

Question No: #6

Let `f : \mathbb{N} \rarr \mathbb{N}` be a mapping defend by $ f(n) = \begin{cases} n+1, & \text{when } n \text{ is odd} \\ n-1, & \text{when } n \text{ is even} \end{cases} $. Show that `f` is a bijective mapping.

Question No: #7

Let `A = \mathbb{R} - {2}` and `B = \mathbb{R} - {1}`. Show that the function `f : A -> B` defined by `f(x)=\frac{x-3}{x-2}` is bijective, where `\mathbb{R}` is the set of all real numbers.

Question No: #8

A mapping `f : \mathbb{R}-{1/3} \rarr \mathbb{R}-{1/3}` is defined by `f(x) = \frac{x+3}{3x-1}`. Then the value of `f^{-1}(4)` is -- (a) `{11/7}`, (b) `{1/4}`, (c) `{7/11}`, (d) none of these.

Question No: #9

A mapping `f : \mathbb{R}-{1/2} \rarr \mathbb{R}-{1/2}` is defined by `f(x) = \frac{x+2}{2x-1}`. Show that `f^{-1}` exists and find formula of `f^{-1}`.

Question No: #10

Let `f : A \rarr A` is a mapping (where `A = {x | -1 \le x \le1}`) defined by `f(x) = \sin\frac{\pi x}{2}`. Show that the mapping `f` is a one-one, onto mapping. Also find a formula that defines `f^{-1}`