Vidaara.orgClass 11 · Mathematics
CodeVID-M11-02-FUN-01
Functions & Real Functions — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
A function assigns each input to:
- A.exactly one output
- B.two outputs
- C.no output
- D.many outputs
2.
The domain of $f(x)=\dfrac1x$ is:
- A.$\mathbb{R}$
- B.$\mathbb{R}\setminus\{0\}$
- C.$[0,\infty)$
- D.$(0,\infty)$
3.
The range of $f(x)=x^2$ is:
- A.$\mathbb{R}$
- B.$[0,\infty)$
- C.$(-\infty,0]$
- D.$\mathbb{R}\setminus\{0\}$
4.
If $f(x)=|x|$, then $f(-3)=$
- A.$-3$
- B.$3$
- C.$0$
- D.$9$
5.
The domain of $\sqrt{x-1}$ is:
- A.$x\ge1$
- B.$x>1$
- C.$x\le1$
- D.$\mathbb{R}$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
If $f(x)=2x+3$, find $f(0)$ and $f(1)$.
7.
Find the domain of $f(x)=\dfrac{1}{x-3}$.
8.
If $f(x)=x^2-1$, find $f(2)$.
9.
Find the range of $f(x)=|x|$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
If $f(x)=x^2+1$, find $f(-2),\ f(0),\ f(2)$.
11.
Find the domain of $f(x)=\sqrt{4-x^2}$.
12.
Simplify $f(x)=\dfrac{x^2-4}{x-2}$ and state its domain.
13.
Find the range of $f(x)=3-x^2$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Let $f(x)=\dfrac{x-1}{x+1}$. Find the domain, $f(0)$, $f(2)$ and check whether $f(1)=0$.
15.
Let $f(x)=x^2$ and $g(x)=2x+1$. Find $(f+g)(x),\ (fg)(x)$ and $(f+g)(2)$.
Answer Key
Section A — Multiple Choice Questions
- (A) exactly one output
- (B) $\mathbb{R}\setminus\{0\}$
- (B) $[0,\infty)$
- (B) $3$
- (A) $x\ge1$
Section B — Short Answer (2 marks)
- $f(0)=3,\ f(1)=5$.
- $\mathbb{R}\setminus\{3\}$.
- $3$.
- $[0,\infty)$.
Section C — Short Answer (3 marks)
- $5,\ 1,\ 5$.
- $[-2,2]$.
- $f(x)=x+2,\ x\ne2$.
- $(-\infty,3]$.
Section D — Long Answer (5 marks)
- Domain $\mathbb{R}\setminus\{-1\}$; $f(0)=-1$; $f(2)=\tfrac13$; $f(1)=0$ (true).
- $(f+g)(x)=x^2+2x+1$; $(fg)(x)=2x^3+x^2$; $(f+g)(2)=9$.
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