SOLUTION: Given the functions 𝑓(𝑥) = √25 − 𝑥 , 𝑔(𝑥) = 𝑥^2+ 9 , ℎ(𝑥) = √𝑥 − 5 a) Obtain the domains of each given function. b) Calculate the domain and rul

Question 1194818: Given the functions 𝑓(𝑥) = √25 − 𝑥 , 𝑔(𝑥) = 𝑥^2+ 9 , ℎ(𝑥) = √𝑥 − 5
a) Obtain the domains of each given function.
b) Calculate the domain and rule of ℎ ∘ 𝑔 .
c) Calculate the domain of 𝑔 ∘ 𝑓 .
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Given the functions:

a) Obtain the domains of each given function.

since given , means must be zero or greater than zero

domain: { element : }

domain: (all real numbers)

since given ,

domain: { element : }

b) Calculate the domain and rule of ℎ ∘ 𝑔 .
ℎ ∘𝑔 =
since is always positive no matter what value is,
domain: (all real numbers)

c) Calculate the domain of 𝑔 ∘ 𝑓 .
𝑔 ∘𝑓 =
domain: (all real numbers)

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