Chapter Study

BCA Semester 1 – Mathematics I – Unit 2: Relation, Functions and Graphs

Comprehensive questions and detailed answers for Unit 2: Relation, Functions and Graphs. Perfect for exam preparation and concept clarity.

Questions

Marks

Back to All Chapters

Find the domain and range of the function

f(x)=\frac{2x+1}{3−x}.

MediumTHEORY5 marks2019(TU FOHSS Final)

a) Define irrational number. Prove that 2 is irrational.\

\ b) For functions f:\mathbb{R}\to\mathbb{R}, \quad f(x)=2x+1

and

g:\mathbb{R}\to\mathbb{R}, \quad g(x)=x^{2}-2

:Find f∘g and g∘f, and verify f∘g≠g∘f.

MediumTHEORY10 marks2019(TU FOHSS Final)

Let $f:R→R$ and $g:R→R$ be defined by $f(x)=2x+3 \text{ and } g(x)=x2−1.$
Find:
$\quad$ i) $\text{f ∘ g}$
$\quad$ ii) $\text{f + g}$
$\quad$ iii) $\text{g ∘ f}$
$\quad$ iv) $\text{f ∘( f ∘ g}$ )

MediumTHEORY10 marks2020(TU FOHSS Final)

Define a function, its domain, and range. Find the domain and range of

f(x) = \sqrt{2 - x - x^2}.

HardNumerical10 marks2021(TU FOHSS Final)

Define a function. Show that the function $f: \mathbb{R} \to \mathbb{R}, \quad f(x) = 3x + 5$ is bijective.

MediumNumerical5 marks2022(TU FOHSS Final)

Define exponential and logarithmic functions. If $f(x)=log⁡ \frac{1−x}{1+x}\space \text{for} −1<x<1, \text{show that}:$

\quad \quad \quad f \begin{pmatrix} \frac{2ab}{1+a^2b^2} \end{pmatrix} =2f(ab)\quad\text{where} |ab|<1.

HardNumerical10 marks2022(TU FOHSS Final)

Find the domain and range of the function: $f(x) = \sqrt{6 - x - x^2}.$

MediumNumerical5 marks2023(TU FOHSS Final)

Prove that the function $f: \mathbb{R} \to \mathbb{R}, \quad f(x) = 3x - 1$ is bijective.

MediumNumerical5 marks2023(TU FOHSS Final)

Find the domain and range of the function: $f(x) = \sqrt{6 - x - x^2}.$

MediumNumerical5 marks2024(TU FOHSS Final)

Showing 9 questions

Sample Questions

Find the domain and range of the function $$ f(x)=\frac{2x+1}{3−x}. $$

Marks: 5Chapter: Unit 2: Relation, Functions and Graphs

a) Define irrational number. Prove that 2 is irrational.\ \[ \ b) For functions f:\mathbb{R}\to\mathbb{R}, \quad f(x)=2x+1 \] and \[ g:\mathbb{R}\to\mathbb{R}, \quad g(x)=x^{2}-2 \]:Find f∘g and g∘f,

Marks: 10Chapter: Unit 2: Relation, Functions and Graphs

Let $f:R→R$ and $g:R→R$ be defined by $f(x)=2x+3 \text{ and } g(x)=x2−1.$\ Find:\ $\quad$i) $\text{f ∘ g}$\ $\quad$ii) $\text{f + g}$\ $\quad$iii) $\text{g ∘ f}$\ $\quad$iv) $\text{f ∘( f ∘ g}

Marks: 10Chapter: Unit 2: Relation, Functions and Graphs

Define a function, its domain, and range. Find the domain and range of \[ f(x) = \sqrt{2 - x - x^2}. \]

Marks: 10Chapter: Unit 2: Relation, Functions and Graphs

Define a function. Show that the function $f: \mathbb{R} \to \mathbb{R}, \quad f(x) = 3x + 5 $ is bijective.

Marks: 5Chapter: Unit 2: Relation, Functions and Graphs

And more questions available on this page.

BCA Semester 1 – Mathematics I – Unit 2: Relation, Functions and Graphs

Sample Questions

Find the domain and range of the function $$ f(x)=\frac{2x+1}{3−x}. $$

a) Define irrational number. Prove that 2 is irrational.\ \[ \ b) For functions f:\mathbb{R}\to\mathbb{R}, \quad f(x)=2x+1 \] and \[ g:\mathbb{R}\to\mathbb{R}, \quad g(x)=x^{2}-2 \]:Find f∘g and g∘f,

Let $f:R→R$ and $g:R→R$ be defined by $f(x)=2x+3 \text{ and } g(x)=x2−1.$\ Find:\ \(\quad\)i) $\text{f ∘ g}$\ \(\quad\)ii) $\text{f + g}$\ \(\quad\)iii) $\text{g ∘ f}$\ \(\quad\)iv) $\text{f ∘( f ∘ g}

Define a function, its domain, and range. Find the domain and range of \[ f(x) = \sqrt{2 - x - x^2}. \]

Define a function. Show that the function \(f: \mathbb{R} \to \mathbb{R}, \quad f(x) = 3x + 5 \) is bijective.