Question

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

Answer 1

domain ; [7,∞),x
Range : [0,∞),y≥0

Answer 2

Domain:
`[7,\infty)`

Range:
`[9,\infty)`

Explanation:

We have been given a function
`f(x)=√(x-7)+9`. We are asked to find the domain and range of our given function.

We know that a square root function is not defined for negative numbers, so domain of our given function would be
`x-7\geq 0`.

`x-7+7\geq 0+7`

`x\geq 7`

Therefore, the domain of our given function is all values of x greater than or equal to 7 that is
`[7,\infty)`.

We know that range of a radical function of form
`f(x)=√(ax+b)+k` is
`f(x)\geq k`.

Upon looking at our given function, we can see that value of k is 9, therefore, the range of our given function is all values of y greater than or equal to 9 that is
`[9,\infty)`.