Question

What are the domain and range of the function f(x)=sqrt(x-7) +9

Answer 1

Answer:

Domain : { x ∈ R : x ≥ 7 }

Range: { f ∈ R : f ≥ 9 }

Step-by-step explanation:

Given function is:

f(x) = $\sqrt{x-7} + 9$

Firstly find the domain of the given function.

Domain is set of all real x's values where given function is defined.

In other words, we exclude all the x's values from all real values where function is undefined.

In case of square root function, inside the square root given expression must be greater or equal to zero.

So,

x - 7 ≥ 0

Solve for x

x ≥ 7

So, domain is all real x when x ≥ 7.

Now find the Range of this function.

Range is set of all output values.

So, lowest value of out put is 9 when x is 7

and maximum value of the function is infinite.

So,

Range is all real f's values when f ≥ 9.

Answer 2

Domain: x ≥ 7

Range (7,9)