Question

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

Answer 1

Domain ; [7,∞),{x|x≥7}
Range : [0,∞),{y|y≥0}

Answer 2

Answer:

Domain: $[7,\infty)$

Range: $[9,\infty)$

Step-by-step explanation:

We have been given a function $f(x)=\sqrt{x-7}+9$. 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 $f(x)=\sqrt{ax+b}+k$ 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 $[9,\infty)$.