Domain and range of functions: Class 11 practice
The domain is every input that gives a real output: exclude values that make a denominator zero or a square root's inside negative. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Inequalities
The idea behind domain and range of functions
The domain is every input that gives a real output: exclude values that make a denominator zero or a square root's inside negative. The range is the set of outputs.
Step-by-step method
- Look for denominators (≠ 0) and even roots (≥ 0).
- Solve those conditions for x.
- Find the range by solving y = f(x) for x.
Worked example 1 (Basic)
Find the domain of f(x) = 1/(x − 9).
- x − 9 ≠ 0
- Domain: all real x except 9
- Answer: ℝ − {9}
Worked example 2 (Standard)
Find the domain of f(x) = √(x − 3).
- x − 3 ≥ 0
- x ≥ 3
- Answer: [3, ∞)
Worked example 3 (Challenge)
Find the range of f(x) = 2 + 1/(x − 5), x ≠ 5.
- 1/(x − 5) takes every real value except 0
- So f(x) ≠ 2
- Answer: ℝ − {2}
Common mistakes and misconceptions
- Forgetting to exclude zeros of the denominator
- Allowing negative inside a square root
Practice questions
- (Basic) Find the domain of f(x) = 1/(x + 5).
- (Basic) Find the domain of f(x) = 1/(x + 7).
- (Standard) Find the domain of f(x) = √(x + 8).
- (Standard) Find the domain of f(x) = √(x − 8).
- (Challenge) Find the range of f(x) = 5 + 1/(x − 1), x ≠ 1.
- (Challenge) Find the range of f(x) = 5 + 1/(x + 5), x ≠ -5.
Answer key with full working
- Q1: x + 5 ≠ 0 → Domain: all real x except -5 → Answer: ℝ − {-5}
- Q2: x + 7 ≠ 0 → Domain: all real x except -7 → Answer: ℝ − {-7}
- Q3: x + 8 ≥ 0 → x ≥ -8 → Answer: [-8, ∞)
- Q4: x − 8 ≥ 0 → x ≥ 8 → Answer: [8, ∞)
- Q5: 1/(x − 1) takes every real value except 0 → So f(x) ≠ 5 → Answer: ℝ − {5}
- Q6: 1/(x + 5) takes every real value except 0 → So f(x) ≠ 5 → Answer: ℝ − {5}
Syllabus note
This skill is listed under "Relations and Functions" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is domain and range of functions in?
"Relations and Functions", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.