Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using
interval notation.
(g◦f)(x) (f ◦g)(x) (f ◦f)(x)
f(x)= 3−x2, g(x)= (√x+1)
1 answer:
Answer:
Given functions,


Since, by the compositions of functions,
1. (g◦f)(x) = g(f(x))


Since, (g◦f) is defined,
If 3 - x² ≥ 0
⇒ 3 ≥ x²
⇒ -√3 ≤ x ≤ √3
Thus, Domain = [-√3, √3]
2. (f◦g)(x) = f(g(x))


Since, (g◦f) is defined,
If x ≥ 0
Thus, Domain = [0, ∞)
3. (f◦f)(x) = f(f(x))




Since, (f◦f) is a polynomial,
We know that,
A polynomial is defined for all real value of x,
Thus, Domain = (-∞, ∞)
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