
What is the domain and range of ?
Answer
449.1k+ views
1 likes
Hint: This type of question depends on the basic concept of trigonometry. We know that and are defined for all real values of . Also the absolute value of both the functions can never be greater than 1 as . Along with this in this question we use and .
Complete step by step solution:
Now, we have to find domain and range of
For this consider,
Now, multiply and divide by we get,
By separating the denominator we can write,
We know that, hence,
Also, we know that,
Hence, we rewrite the given function as .
As we know that the function is defined for all real values of . Thus the domain of is:
In similar manner we can say that the function is also defined for all values of and hence for all values of . Thus we can say that the domain of the function is:
Also we know that the absolute value of can never be greater than 1. So we have:
Thus, the value of the function lies from to .
Hence, the range of is:
Hence, the domain and range of
Note: In this type of question students may make a conversion of into . Students may consider the function as it is and try to find out the domain and range or one may directly divide by . Students have to take care during multiplication and division by as well as in conversion also.
Complete step by step solution:
Now, we have to find domain and range of
For this consider,
Now, multiply and divide by
By separating the denominator we can write,
We know that,
Also, we know that,
Hence, we rewrite the given function
As we know that the function
In similar manner we can say that the function
Also we know that the absolute value of
Thus, the value of the function
Hence, the range of
Hence, the domain and range of
Note: In this type of question students may make a conversion of
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE
