Question

What is the range of the function y=square root x+5

Answer 1

Range of the given function is [ 5 , ∞ )

Explanation:

Given function is
`y\:=\:√(x)+5`

We need to find Range of the given function.

The Range of function is the set of all possible values of the dependent variable ( here, y ) , after substituting the value of domain.

We know that square root can not have negative value. So, Domain of the given function is all non negative real number.

That is Domain = { x : x ∈ R and x ≥ 0 } = [ 0 , ∞ )

Now for range,

put x = 0 in given function,

`y\:=\:√(0)+5=5`

⇒ Minimum value of range is 5

put x = ∞ in given function,

`y\:=\:√(\infinity)+5=\infinity+5=\infinity`

⇒ Maximum value of range is ∞

Thus, Range = { y : y ∈ R and y ≥ 5 } = [ 5 , ∞ )

Therefore, Range of the given function is [ 5 , ∞ )