Question

The domain of f(x,y)=ln( x 2 +y 2 ​ ) is a. {(x,y)∈R 2 ∣x≥0,y≥0} b. R 2 −{(0,0)} c. {(x,y)∈R 2 ∣x≤0,y≤0} d. R 2

Answer 1

The domain of the function f(x, y) = ln(x2 + y2) will be all the x and y values for which the function is defined. The function is undefined at (0,0) hence the domain will be all real numbers except (0,0), representing option 'b'.

Step-by-step explanation:

The domain of a function is the set of all possible input values (usually x-values) that will give a valid output value. In other words, the domain is the range of values for which the function is defined. In the given function f(x, y) = ln(x2 + y2), you are taking the natural logarithm (or ln) of the sum of squares of x and y. The natural logarithm (ln) is undefined for negative numbers and zero. It means, x2 + y2 can't be zero or negative. Therefore, in this case the only inputs x, y we can't have are those which result in zero when plugged into the formula, which happens at (0, 0). Hence, the domain is all real numbers except where (0, 0) which corresponds to option b. R2 - {(0,0)}.

Learn more about Domain of function