### 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)= x^{2}+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