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

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Answer 1 · 2018-02-06T11:10:48

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

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:

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

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