For which pairs of numbers (x.y) is the function given below defined?

#(x^2+y^2)^(1/2) + (x^2+y^2-1)^(1/2)#

1 Answer
dhruv ahlawat
Mar 4, 2018

for #x^2 + y^2 >=1#

Explanation:

since we cannot take a square root of a negative number or raise it to a half power (unless using complex mathematics),
#(x^2 + y^2 -1)# should be positive and if it is, (#x^2 + y^2# )will be positive too

therefore, this function will be defined for all #x^2 + y^2 >= 1#

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