Question

Given functions 𝑓(𝑥) = 6 + √𝑥 − 4 and 𝑔(𝑥) =

10

𝑥−5

. 

Determine the domain and range of 𝑓(𝑥) and 𝑔(𝑥)

Answer 1

Functions have the following form: $f(x)=6+\sqrt{x-4},$ $g(x)=10(x-5)$. The domain of the first function is $[4,+\infty)$, since the value under the square root must be nonnegative. The domain of the second function is $\mathbb{R}$, since it is a linear function. The range of the first function is $[6,+\infty)$, since the square root is always nonnegative. The range of the second function is $\mathbb{R}$.