Respuesta :
Answer:
Domain: [tex][7,\infty)[/tex]
Range: [tex][9,\infty)[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=\sqrt{x-7}+9[/tex]. 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 [tex]x-7\geq 0[/tex].
[tex]x-7+7\geq 0+7[/tex]
[tex]x\geq 7[/tex]
Therefore, the domain of our given function is all values of x greater than or equal to 7 that is [tex][7,\infty)[/tex].
We know that range of a radical function of form [tex]f(x)=\sqrt{ax+b}+k[/tex] is [tex]f(x)\geq k[/tex].
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 [tex][9,\infty)[/tex].
