Explain algebraic operations on functions . Dom? Explain algebraic operations on functions . Dom? TYP any t i. a then and are then the prod If f g are functions, f/g is defined dom dom(g) n I x: O' by S. offtmcrions Let f: A B and C be functions. then go/ : A —9 C defined Igor ' goo)). We have the following tormulae for domains Of futrtions. 2. dom (f g) = dornfn dom g 4. dom = domfn Note that ifge/is defined. may not be defined. For example if f: A —+ B and g : B C then go/ is defilWd but/ög is not. Let g: R —i R and g: R —i R be dctined by coss and go) • v'. Then go' (x) D geos cosh and/og (x) e 'Illus even if jog and gof "c both defined it is not necessary that go/ Share with your friends Share 0 Aarushi Mishra answered this Algrebraic operations are addition/ subtraction, multipication and division,etc When we define these operations on functions, they are called algrebraic operations on functions.f+gx=fx+gx additionf-gx=fx-gx subtractionfgx=fx gx multipicationfgx=fxgx divisionfx=fxDomain for functions obtained by addition, subtraction and mutlipication is intersection of domains of the two function, i.e. dom f∩dom gIn fgx=fxgx since denomniator cannot be zero so domain is dom f∩dom g∩x:gx≠0domain of fx=fx is x:fx≥0 because the qunatity inside square root should be non-negativeIn addition to his we define to extra algebraic operationsComposition:fogx=fgx, i.e. first put value if x in gx and then put the value obtain from gx into fx. Its domain will be all values of x such that gx is in domain of fx 0 View Full Answer
