Question
Find the domain and range of $f(x)=|2 x-3|-3$.
✓
Answer
Given, $\mathrm{f}(\mathrm{x})=|2 \mathrm{x}-3|-3$
The domain of the expression is all real number except where the expression is undefined. In this case, there is not real number that makes the expression undefined.
$\therefore$ Domain of $\mathrm{f}=(-\infty, \infty)=\mathrm{R}$
The absolute value of expression has a 'V' shape. The range of a positive absolute value expression starts at its vertex and extends to infinity.
Range of $\mathrm{f}=[-3, \infty)$ or $\{y: y \geq-3\}$
The domain of the expression is all real number except where the expression is undefined. In this case, there is not real number that makes the expression undefined.
$\therefore$ Domain of $\mathrm{f}=(-\infty, \infty)=\mathrm{R}$
The absolute value of expression has a 'V' shape. The range of a positive absolute value expression starts at its vertex and extends to infinity.
Range of $\mathrm{f}=[-3, \infty)$ or $\{y: y \geq-3\}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Rohit is the husband of Vanshika. Sumita is the sister of Rohit. Anushka is the sister of Vanshika. How Anushka is related to Rohit?
Reduce the equation $3 x-2 y+4=0$ to intercept form. Hence, find the length of the segment intercepted between the axes.
→Mr. Sharma in Delhi is using an MTNL connection with a monthly plan of ₹ 240 , which has no free calls. The call charges are ₹ 1 per minute. Calculate the telephone bill payable for Mr. Sharma if he talks for 470 minutes in a month. Assume the broadband charges to be Nil. A GST of $18 \%$ is levied on the total bill amount.
→Co-efficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16 respectively. What are their arithmetic mean?
Divide ₹ 15,500 into two parts such that if one part be lent out at $15 \%$ per annum and the other at $24 \%$ per annum, the total annual income is ₹ 3,000 .
→Mr. Kohli, a citizen of India, is an export manager of Arjun Overseas Limited, an Indian Company, since 1.5.2014. He has been regularly going to USA for export promotion. He spent the following days in U.S.A. for the last five years :
Determine his residential status for assessment year 2019-20 assuming that prior to 1.5.2014 he had never travelled abroad.
| Previous year ended | No. of days spent in USA |
| 31.3.2015 | 317 days |
| 31.3.2016 | 150 days |
| 31.3.2017 | 271 days |
| 31.3.2018 | 311 days |
| 31.3.2019 | 294 days |
Find the mean about median for the following profits (in ₹ 1000 ) of a firm during a week
82,56,75,70,52,80,68
82,56,75,70,52,80,68
Find the domain and the range of the given function: $\mathrm{f}(\mathrm{x})=\sqrt{x^{2}-4}$
→Simplify:
$\frac{1}{1+a^{m-n}+a^{m-p}}+\frac{1}{1+a^{n-m}+a^{n-p}}+\frac{1}{1+a^{p-m}+a^{p-n}}$
→$\frac{1}{1+a^{m-n}+a^{m-p}}+\frac{1}{1+a^{n-m}+a^{n-p}}+\frac{1}{1+a^{p-m}+a^{p-n}}$
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at $4 \%$ per annum is ₹ 1. Find the sum.
→