Could you please help me with question 47&53 ? thank you

Determine the domains of the functions in Exercises 47-56, and find where the functions are continuous. 54. f 2 47. x2 - y2 48. f (x, y, z) = xy2 F(x, y) x ty -z 55. 49. f (x, y) = Vx2 + y 50. f (x, y, z) = In(x2 + y2 +22) 51. f (x, y, 2) = sin (x + y +2) 52. f (x, 1, 2 ) = e "/: 56. VX ty+z if (x, y) = (0,0) 53. f (x, y ) = /x =+y 0, if (x, y) = (0, 0) Applications The ideal gas law states that the pressure, P. volume, V, tem- (b perature in degrees Kelvin, 7, and amount, /, of a gas are