02 Relations and Functions
Exercise 3
Question:
Which of the following relations are functions? Give reasons. If it is a function determine its domain and range (i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)} (ii) {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)} (iii) {(1,3),(1,5),(2,5)}
Answer:
(i) This is not a function because the input value of 2, 5, 8, 11, 14 and 17 all have the same output value of 1.
Domain: {2, 5, 8, 11, 14, 17} Range: {1}
(ii) This is a function because each input value has a unique output value.
Domain: {2, 4, 6, 8, 10, 12, 14} Range: {1, 2, 3, 4, 5, 6, 7}
(iii) This is not a function because the input value of 1 appears twice with different output values.
Domain: {1, 2} Range: {3, 5}
Question:
The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by t(C)=59C+32° Find : (i) t(0°) (ii) t(28°) (iii) t(−10°) (iv) The value of C when t(C)=212°F
Answer:
(i) t(0°) = 59*0 + 32 = 32°F
(ii) t(28°) = 59*28 + 32 = 1656°F
(iii) t(−10°) = 59*(-10) + 32 = -502°F
(iv) 212 = 59C + 32 C = (212-32)/59 C = 3.38°C
Question:
Find the range of each of the following functions (i) f(x)=2−3x, x∈R,x>0 (ii) f(x)= x2+2, x is a real number (iii) f(x)=x,x is a real number
Answer:
(i) Range: f(x) ≥ 0
(ii) Range: All real numbers
(iii) Range: All real numbers
Question:
A function f is defined by f(x)=2x−5. Write down the values of (i) f(0) (ii) f(7) (iii) f(−3)
Answer:
(i) f(0) = 2(0) − 5 = -5
(ii) f(7) = 2(7) − 5 = 9
(iii) f(−3) = 2(-3) − 5 = -7
JEE NCERT Solutions (Mathematics)
01 Sets
02 Relations and Functions
03 Trigonometric Functions
04 Principle of Mathematical Induction
05 Complex Numbers and Quadratic Equations
06 Linear Inequalities
07 Permutations and Combinations
08 Binomial Theorem
09 Sequences and Series
10 Straight Lines Exercise
10 Straight Lines Miscellaneous
11 Conic Sections
12 Introduction to Three Dimensional Geometry
13 Limits and Derivatives
14 Mathematical Reasoning
15 Statistics
16 Probability