Q. 105.0( 1 Vote )

Let f(x) = x2 and g(x) = 2x + 1 be two real functions. Find (f + g)(x), (f – g)(x), (fg)(x) and .

Answer :

Given f(x) = x2 and g(x) = 2x + 1


Both f(x) and g(x) are defined for all x R.


Hence, domain of f = domain of g = R


i. f + g


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


(f + g)(x) = x2 + 2x + 1


(f + g)(x) = (x + 1)2


Clearly, (f + g)(x) is defined for all real numbers x.


Domain of (f + g) is R


Thus, f + g : R R is given by (f + g)(x) = (x + 1)2


ii. f – g


We know (f – g)(x) = f(x) – g(x)


(f – g)(x) = x2 – (2x + 1)


(f – g)(x) = x2 – 2x – 1


Clearly, (f – g)(x) is defined for all real numbers x.


Domain of (f – g) is R


Thus, f – g : R R is given by (f – g)(x) = x2 – 2x – 1


iii. fg


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


(fg)(x) = x2(2x + 1)


(fg)(x) = 2x3 + x2


Clearly, (fg)(x) is defined for all real numbers x.


Domain of fg is R


Thus, fg : R R is given by (fg)(x) = 2x3 + x2


iv.


We know



Clearly, is defined for all real values of x, except for the case when 2x + 1 = 0.


2x + 1 = 0


2x = –1



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


Thus, the domain of = R –


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