Question

13 3) The range of function f : RR, f(x) = x2 + 2 is
​

Answer 1

Step-by-step explanation:

Domain

The domain of a function includes every possible value of

x

that will not involve division by zero or make a complex number. You can only get complex numbers if you can turn the stuff inside of the square root negative. Because there is no denominator, you will never divide by zero. What about complex numbers? You have to set the inside of the square root to less than zero and solve:

4

−

x

2

<

0

(

2

+

x

)

(

2

−

x

)

<

0

or when

2

+

x

<

0

and

2

−

x

<

0

. That is, when

x

<

−

2

and

x

>

2

So your domain is

[

−

2

,

2

]

. Both the

2

and

−

2

are included, because the stuff inside the square root is allowed to be zero.