To determine the domain of the function, we need to find the values of x that are valid inputs for both functions f(x) and g(x).
For f(x), the only value of x that is not allowed is x = 4, since it would make the denominator of the fraction zero.
For g(x), the only value of x that is not allowed is x = 0, since it would make the denominator of the fraction zero.
Therefore, the domain of the function f(g(x)) is all real numbers except x = 0 and x = 4.
Domain: x ≠ 0, x ≠ 4
Determine the domain of the function left-parenthesis lower f circle lower g right-parenthesis left-parenthesis x right-parenthesis where lower f left-parenthesis x right-parenthesis equals Start Fraction 3 x minus 1 over x minus 4 End Fraction and lower g left-parenthesis x right-parenthesis equals Start Fraction x plus 1 over x End Fraction.
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