What is the domain and range of #f(x,y) = 3 + sin(sqrt y-e^x)#?

1 Answer
Feb 6, 2018

Answer:

Range: #{f(x,y)in RR: 2 <= f(x,y) <= 4}#
Domain: #{(x,y)inRR^2:y>=0}#

Explanation:

Assuming a real valued function, the range of the sine function is #-1 <= sin(u)<=1#, therefore, #f(x,y)# can vary from #3 +-1# and the range is:

#{f(x,y)in RR: 2 <= f(x,y) <= 4}#

The domain for y is restricted by the fact that the argument for the radical must be greater than or equal to zero:

#{yinRR:y>=0}#

The value of x can be any real number:

#{(x,y)inRR^2:y>=0}#