Q. 1 B5.0( 2 Votes )

Find f + g, f – g, cf (c R, c ≠ 0), fg, 1/f and f/g in each of the following:

and

Answer :

and


We have f(x) : [1, ∞) R+ and g(x) : [–1, ∞) R+ as real square root is defined only for non-negative numbers.


(a) 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 = [1, ∞) [–1, ∞)


Domain of f + g = [1, ∞)


Thus, f + g : [1, ∞) R is given by


(b) 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 = [1, ∞) [–1, ∞)


Domain of f – g = [1, ∞)


Thus, f – g : [1, ∞) R is given by


(c) cf (c R, c ≠ 0)


We know (cf)(x) = c × f(x)



Domain of cf = Domain of f


Domain of cf = [1, ∞)


Thus, cf : [1, ∞) R is given by


(d) fg


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




Domain of fg = Domain of f Domain of g


Domain of fg = [1, ∞) [–1, ∞)


Domain of fg = [1, ∞)


Thus, fg : [1, ∞) R is given by


(e)


We know



Domain of = Domain of f


Domain of = [1, ∞)


Observe that is also undefined when x – 1 = 0 or x = 1.


Thus, : (1, ∞) R is given by


(f)


We know




Domain of = Domain of f Domain of g


Domain of = [1, ∞) [–1, ∞)


Domain of = [1, ∞)


Thus, : [1, ∞) R is given by


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