Answer:
The domain of f(x) is all real numbers greater than or equal to -2
Step-by-step explanation:
We have been given that
[tex]f(x)=2(x)^2+5\sqrt{x+2}[/tex]
Domain is the set of x values for which the function is defined.
The given function is the combination of a square and square root function.
Square function is defined for all real values. Whereas, the square root function is defined for only positive values.
Therefore, the function is defined when
[tex]x + 2\geq0[/tex]
Subtract 2 to both sides
[tex]x\geq-2[/tex]
Hence, the domain of f(x) is all real numbers greater than or equal to -2
