If f(x)=(3)/(x-2) and g(x)=√(x+1), find the domain of f ∘g . (A) x ≥-1 (B) x ≠2 (C) x ≥-1, x ≠2

step 1 They're given that f of x is, sorry, this is a 3, 3 over x minus 2, G of x is equal to square wi

If f(x)=(3)/(x-2) and g(x)=√(x+1), find the domain of f ∘g ....

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Key Concepts

Rational Function Domain

A rational function like f(x) = 3/(x - 2) is undefined when its denominator is zero. Therefore, it is necessary to exclude any values of x that satisfy the equation x - 2 = 0. When dealing with composite functions, any additional restrictions from substituting the inner function into the outer function must be considered.

Square Root Function Domain

A square root function, such as g(x) = ?(x + 1), is defined only when the expression under the square root is non-negative. This translates to setting up and solving an inequality (x + 1 ? 0) which restricts the domain of the function to values meeting this condition.

Composite Functions

Composite functions involve applying one function to the results of another, denoted as (f ? g)(x) = f(g(x)). When working with composite functions, it is crucial to determine the domain by ensuring that the outputs of the inner function fit within the domain of the outer function.

Domain Restrictions

Determining the domain of a composite function requires considering the restrictions imposed by both functions. This means identifying the values that make the inner function defined and also ensuring that those values, when used in the outer function, do not lead to undefined expressions.

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