– g ) ( x ), (fg ) ( x ), f g Solution We have, ( f + g ) ( x ) = x + x + , ( f – g ) ( x ) = x – x – , ( f g) ( x ) = x ( x + ) = x + x , f g x + , x ≠ Example Let f ( x ) = x and g ( x ) = x be two functions defined over the set of non- negative real numbers. Find ( f + g ) ( x ), ( f – g ) ( x ), ( fg ) ( x ) and f g ( x ). Solution We have ( f + g ) ( x ) = x + x , ( f – g ) ( x ) = x – x , ( fg ) x = x( x ) and f g – , x ≠ MATHEMATICS EXERCISE . .
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. {( , ), ( , ), ( , ), ( , ), ( , ), ( , )} {( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , )} (iii) {( , ), ( , ), ( , )}.
. Find the domain and range of the following real functions: f ( x ) = – x f ( x ) = . A function f is defined by f ( x ) = x – . Write down the values of f ( ), (ii) f ( ), (iii) f (– ).
. The function ‘ t ’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by t (C) = 9C + . Find t ( ) (ii) t ( ) (iii) t (– ) (iv) The value of C, when t (C) = . .
Find the range of each of the following functions. f ( x ) = – x, x ∈ R , x > . f ( x ) = x