Domain and Range of the functions

[kidia]

Please can anybody help me on this two functions it confuse me because has two and thee variables.

Find the Domain and Range of each of the following functions

a)f(x,x)=$$\sqrt{\frac{x-y}{x+y}}$$

b)f(x,y)=$$\[in{(x^2+y^2+z^2)}$$

 

[leon1127]

a) x+y not equal to zero and (x-y/x+y)>=0, range should be all positive real

b) i assume that is Ln[x^2+y^2+z^2] then the argument can't be non-positive.

These functions map to one demensional space, so the range should be clear and obvious. Domain is similar to R^1, like postive argument under square root, divid by 0 etc.

 

[tacman]

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a) The domain of this function is all real numbers except for values of x and y that make the expression inside the square root negative (since we cannot take the square root of a negative number). So the domain can be represented as: x+y > 0 and x-y > 0. The range would be all real numbers greater than or equal to 0, since the square root will always result in a positive number.

b) The domain of this function would be all real numbers for x, y, and z. The range would be all real numbers greater than or equal to 0, since the function is taking the natural logarithm of a positive number (since the input is squared).