Q. 95.0( 1 Vote )

Let f : [0, ∞) R and g : R R be defined by and g(x) = x. Find f + g, f – g, fg and

Answer :

Given and g(x) = x


Domain of f = [0, ∞)


Domain of g = R


i. f + g


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



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


Domain of f + g = [0, ∞) R


Domain of f + g = [0, ∞)


Thus, f + g : [0, ∞) R is given by


ii. f – g


We know (f – g)(x) = f(x) – g(x)



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


Domain of f – g = [0, ∞) R


Domain of f – g = [0, ∞)


Thus, f – g : [0, ∞) R is given by


iii. fg


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





Clearly, (fg)(x) is also defined only for non-negative real numbers x as square of a real number is never negative.


Thus, fg : [0, ∞) R is given by


iv.


We know





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


When x = 0, will be undefined as the division result will be indeterminate.


Domain of = [0, ∞) – {0}


Domain of = (0, ∞)


Thus, : (0, ∞) R is given by


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