Q. 184.4( 7 Votes )

Let f, g: R R be defined, respectively by f(x) = x + 1 and g(x) = 2x – 3. Find f + g, f – g and.

Find the domain in each case.

Answer :

Given f(x) = x + 1 and g(x) = 2x – 3


Clearly, both f(x) and g(x) exist for all real values of x.


Hence, Domain of f = Domain of g = R


Range of f = Range of g = R


i. f + g


We know (f + g)(x) = f(x) + g(x)


(f + g)(x) = x + 1 + 2x – 3


(f + g)(x) = 3x – 2


Domain of f + g = Domain of f Domain of g


Domain of f + g = R R


Domain of f + g = R


Thus, f + g : R R is given by (f + g)(x) = 3x – 2


ii. f – g


We know (f – g)(x) = f(x) – g(x)


(f – g)(x) = x + 1 – (2x – 3)


(f – g)(x) = x + 1 – 2x + 3


(f – g)(x) = –x + 4


Domain of f – g = Domain of f Domain of g


Domain of f – g = R R


Domain of f – g = R


Thus, f – g : R R is given by (f – g)(x) = –x + 4


iii.


We know



Clearly, is defined for all real values of x, except for the case when 2x – 3 = 0 or.


When, will be undefined as the division result will be indeterminate.


Thus, domain of = R –


Thus, : R – R is given by

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