What is the domain of the inverse function of f(x) = (-12x - 7)/(x + 3)?

What is the domain of the inverse function of f(x) = (-12x - 7)/(x + 3)?

• A. All real numbers except x = -12
• B. All real numbers
• C. [-12, ∞)
• D. (-∞, -12)

Answer: (A)

To determine the domain of the inverse function of \( f(x) = \frac{-12x - 7}{x + 3} \), we first need to understand the function itself, particularly any restrictions on its domain. The function is a rational function, and the only restriction occurs when the denominator equals zero. Setting the denominator equal to zero, we find that: \[ x + 3 = 0 \implies x = -3. \] Thus, the function is not defined at \( x = -3 \). This tells us that the domain of \( f(x) \) includes all real numbers except for \( x = -3 \). When dealing with inverse functions, the roles of the input and output are switched. Therefore, the domain of the inverse function corresponds to the range of the original function. Since \( f(x) \) is continuous and only has one discontinuity at \( x = -3 \), we can find the value of \( f(-3) \) to identify another point of note. However, we can observe that the function \( f(x) \) approaches a vertical asymptote at \( x = -3 \) but maintains continuity elsewhere. To find the range, we

To determine the domain of the inverse function of ( f(x) = \frac{-12x - 7}{x + 3} ), we first need to understand the function itself, particularly any restrictions on its domain. The function is a rational function, and the only restriction occurs when the denominator equals zero. Setting the denominator equal to zero, we find that:

[ x + 3 = 0 \implies x = -3. ]

Thus, the function is not defined at ( x = -3 ). This tells us that the domain of ( f(x) ) includes all real numbers except for ( x = -3 ).

When dealing with inverse functions, the roles of the input and output are switched. Therefore, the domain of the inverse function corresponds to the range of the original function. Since ( f(x) ) is continuous and only has one discontinuity at ( x = -3 ), we can find the value of ( f(-3) ) to identify another point of note. However, we can observe that the function ( f(x) ) approaches a vertical asymptote at ( x = -3 ) but maintains continuity elsewhere.

To find the range, we