How To Find H(X)=G(F(X)): A Guide To Optimizing Domains In Math Compositions

domains that need to be checked when finding h(x)=g(f(x))

f(x) and h(x) only (NOT g(x))

When finding h(x)=g(f(x)), there are several domains that need to be checked:

1. Domain of f(x): F(x) is the inner function in the composition, so we need to check its domain first. The domain of f(x) is the set of all values that x can take without causing any mathematical errors in the expression.
2. Range of f(x): Since g(x) is the outer function, it is important to determine whether all possible outputs of the inner function will be accepted by the outer function. Therefore, it is essential to check what the range of f(x) is and whether it is within the domain of g(x).
3. Domain of g(x): The domain of g(x) is the set of all inputs that g(x) can accept without causing any mathematical errors in the expression.
4. Overall domain: Once we have established the domains of both f(x) and g(x), we need to check if there are any values of x that cannot be used in the expression.

It is important to check all the domains thoroughly as any discrepancies may result in an undefined function or an incorrect answer.

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