(g o f)(x)

Question

f(x) = x-7
g(x) = square root of x-2

domain of (g o f)(x) in interval notation

equation rule for (g o f)(x) =

Answer 1

f(x) = x - 7

g(x) = √(x - 2)

 

 

(g o f)(x) =

 

g(f(x)) =

 

g(x - 7) =

 

√(x - 7 - 2) = √(x - 9)

 

 

The number under the square-root must be a positive number, or it will not be a real number.

 

x - 9 ≥ 0

x ≥ 9

 

Your domain is   [9, ∞)