Question

The domain for f(x) is all real numbers greater than or equal to ___ ?

Answer 1

You must set each part of the function equal to zero.

5√(x+2) = x is greater than or equal to -2

So the domain is greater than or equal to -2

Answer 2

The domain of f(x) is all real numbers greater than or equal to -2

Explanation:

We have been given that

`f(x)=2(x)^2+5√(x+2)`

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

`x + 2\geq0`

Subtract 2 to both sides

`x\geq-2`

Hence, the domain of f(x) is all real numbers greater than or equal to -2