Relations and Functions (Part – 2)

This comprehensive course is designed to help you master essential mathematical concepts. Throughout your studies, you'll explore a variety of topics, including One-to-One and Onto Functions, Composite Functions, and the Inverse of a Function.
To deepen your understanding of these concepts and prepare for related examinations, this course includes a series of practice assignments. These assignments feature carefully selected questions from a range of authoritative sources, including NCERT Textbook exercises, NCERT Examples, Board's Question Bank, RD Sharma, NCERT Exemplar, and more.
With the knowledge and skills you'll gain from this course, you'll be well-equipped to tackle any related mathematical challenges with confidence.

8 hours 22 minutes Course Duration
English Syllabus medium
Hindi + English Explanation
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Course Content

Lecture – 2


Questions Discussed:

Question 6. the injectivity and surjectivity of the following functions: (N)
  a. f:\mathbf{N}\to \mathbf{N} given by f(x)={{x}^{2}}
  b. f:\mathbf{Z}\to \mathbf{Z} given by f(x)={{x}^{2}}
  c. f:\mathbf{R}\to \mathbf{R} given by f(x)={{x}^{2}}
  d. f:\mathbf{N}\to \mathbf{N} given by f(x)={{x}^{3}}
  e. f:\mathbf{Z}\to \mathbf{Z} given by f(x)={{x}^{3}}

Question 7.Prove that the Greatest Integer Function f:\mathbf{R}\to \mathbf{R}, given by f(x)=[x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x. (N)

Question 8.Show that the Modulus Function f:\mathbf{R}\to \mathbf{R}, given by f(x)=\,|x|, is neither one-one nor onto, where | x | is x, if x is positive or 0 and | x | is -x, if x is negative. (N)

Question 9.Show that the Signum Function f:\mathbf{R}\to \mathbf{R}, given by {\displaystyle f(x)=\begin{cases} 1, & \text{ if } x > 0 \\ 0, & \text{ if } x=0 \\ -1, & \text{ if } x < 0 \end{cases} } is neither one-one nor onto. (N)

Question 10.In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer. (N)
  a. f:\mathbf{R}\to \mathbf{R} defined by f(x)=3-4x
  b. f:\mathbf{R}\to \mathbf{R} defined by f(x)=1+{{x}^{2}}

Question 11. Let f:\mathbf{R}\to \mathbf{R} be defined as f(x)={{x}^{4}}. Choose the correct answer. (N)
  a.f is one-one onto
  b.f is one-one but not onto
  c.f is many-one onto
  d.f is neither one-one nor onto.

Question 12.Let f:\mathbf{R}\to \mathbf{R} be defined as f(x)=3x. Choose the correct answer.(N)
  a.f is one-one onto
  b.f is one-one but not onto
  c.f is many-one onto
  d.f is neither one-one nor onto.